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Search: id:A048675
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| A048675 |
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Binary encoding of factorizations, a(n) = bef(n). |
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+0
8
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| 0, 1, 2, 2, 4, 3, 8, 3, 4, 5, 16, 4, 32, 9, 6, 4, 64, 5, 128, 6, 10, 17, 256, 5, 8, 33, 6, 10, 512, 7, 1024, 5, 18, 65, 12, 6, 2048, 129, 34, 7, 4096, 11, 8192, 18, 8, 257, 16384, 6, 16, 9, 66, 34, 32768, 7, 20, 11, 130, 513, 65536, 8, 131072, 1025, 12, 6, 36, 19
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Gives bijective mapping if the source sequence is square-free (A048672), or there are max two prime divisors or one p with max exponent being 2 (A048623 and A048639).
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FORMULA
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a(1) = 0, a(n) = 1/2 * (e1*2^i1 + e2*2^i2 + ... + ez*2^iz) if n = p_i1^e1*p_i2^e2*...*p_iz^ez, where p_i isi-th prime. (e.g. p1=2, p2=3)
Totally additive with a(p^e) = 2^(PrimePi(p)-1), where PrimePi(n) = A000720(n).
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MAPLE
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nthprime := proc(n) local i; if(isprime(n)) then for i from 1 to 1000000 do if(ithprime(i) = n) then RETURN(i); fi; od; else RETURN(0); fi; end; # nthprime(2) = 1, nthprime(3) = 2, nthprime(5) = 3, etc. - this is also A049084.
A048675 := proc(n) local s, d; s := 0; for d in ifactors(n)[ 2 ] do s := s + d[ 2 ]*(2^(nthprime(d[ 1 ])-1)); od; RETURN(s); end; bef := A048675; # bef = Binary Encode Factorization.
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CROSSREFS
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Cf. A048623, A048676.
Sequence in context: A096441 A100824 A163227 this_sequence A162474 A048676 A049287
Adjacent sequences: A048672 A048673 A048674 this_sequence A048676 A048677 A048678
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jul 14 1999
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