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Search: id:A064547
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| A064547 |
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Sum of binary digits (or count of 1-bits) in the exponents of the prime factorization of n. |
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+0
4
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| 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 3, 3
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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This sequence is different from A058061 for n containing 6th, 8th, ..., k-th powers in its prime decomposition, where k runs through the integers missing from A064548.
For n > 1, n is a product of a(n) distinct members of A050376. - Matthew Vandermast (ghodges14(AT)comcast.net), Jul 13 2004
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,2000
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EXAMPLE
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a(54)=3 since 54=2^1 * 3^3 with exponents (1) and (11) in binary
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MAPLE
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Maple program from N. J. A. Sloane (njas(AT)research.att.com), Dec 20 2007:
expts:=proc(n) local t1, t2, t3, t4, i; if n=1 then RETURN([0]); fi; if isprime(n) then RETURN([1]); fi; t1:=ifactor(n); if nops(factorset(n))=1 then RETURN([op(2, t1)]); fi; t2:=nops(t1); t3:=[]; for i from 1 to t2 do t4:=op(i, t1); if nops(t4) = 1 then t3:=[op(t3), 1]; else t3:=[op(t3), op(2, t4)]; fi; od; RETURN(t3); end;
A000120 := proc(n) local w, m, i; w := 0; m := n; while m > 0 do i := m mod 2; w := w+i; m := (m-i)/2; od; w; end:
LamMos:= proc(n) local t1, t2, t3, i; t1:=expts(n); add( A000120(t1[i]), i=1..nops(t1)); end;
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MATHEMATICA
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Table[Plus@@(DigitCount[Last/@FactorInteger[k], 2, 1]), {k, 105}]
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PROGRAM
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(PARI) SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } baseE(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { for (n=1, 2000, f=factor(n)~; a=0; for (i=1, length(f), a+=SumD(baseE(f[2, i], 2))); write("b064547.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 18 2009]
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CROSSREFS
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Cf. A000028, A000379, A058061.
Adjacent sequences: A064544 A064545 A064546 this_sequence A064548 A064549 A064550
Sequence in context: A160980 A065031 A058061 this_sequence A086435 A099305 A033109
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 09 2001
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