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Search: id:A141567
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| A141567 |
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Bases and exponents in the prime decomposition of n replaced by nonprimes with these indices. |
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1
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| 0, 1, 4, 1, 8, 4, 10, 1, 4, 8, 16, 4, 20, 10, 32, 1, 25, 4, 27, 8, 40, 16, 33, 4, 8, 20, 256, 10, 40, 32, 44, 1, 64, 25, 80, 4, 51, 27, 80, 8, 56, 40, 58, 16, 32, 33, 64, 4, 10, 8, 100, 20, 72, 256, 128, 10, 108, 40, 80, 32, 82, 44, 40, 1, 160, 64, 90, 25, 132, 80, 94, 4, 96, 51, 32
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Start from the prime decomposition of n, not writing down exponents which equal 1; that is the list 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3,.. Replace each number i in this representation by the nonprime r(i)=A141468(i). This generates the sequence of a(n), namely r(1), r(2), r(3), r(2)^r(2), r(5), r(2)*r(3), r(7), r(2)^r(3), r(3)^r(2), r(2)*r(5), r(11), r(2)^r(2)*r(3),...
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MAPLE
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A141468 := proc(n) option remember ; local a; if n <= 2 then n-1 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: A := proc(n) local a, p, e, q, ifs ; ifs := ifactors(n)[2] ; if n = 1 then RETURN(0) fi; a := 1; for p in ifs do q := A141468(op(1, p)) ; if op(2, p) > 1 then e := A141468(op(2, p)) ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 120 do printf("%d, ", A(n)) ; od: # R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 21 2008
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CROSSREFS
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Cf. A000040, A002808, A141468.
Sequence in context: A096051 A060440 A021709 this_sequence A134417 A116080 A143820
Adjacent sequences: A141564 A141565 A141566 this_sequence A141568 A141569 A141570
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 17 2008
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EXTENSIONS
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Edited and corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 21 2008
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