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Search: id:A141568
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| A141568 |
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Bases and exponents in the prime decomposition of n replaced by nonprimes with these indices. |
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+0
1
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| 1, 4, 6, 256, 9, 24, 12, 4096, 1296, 36, 18, 1536, 21, 48, 54, 65536, 26, 5184, 28, 2304, 72, 72, 34, 24576, 6561, 84, 46656, 3072, 42, 216, 45, 262144, 108, 104, 108, 331776, 52, 112, 126, 36864, 57, 288, 60, 4608, 11664, 136, 65, 393216, 20736, 26244, 156
(list; graph; listen)
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OFFSET
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1,2
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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)=A018252(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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A018252 := proc(n) option remember ; local a; if n = 1 then 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(1) fi; a := 1; for p in ifs do q := A018252(op(1, p)) ; if op(2, p) > 1 then e := A018252(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, A018252.
Sequence in context: A070156 A081970 A076098 this_sequence A113838 A056831 A027717
Adjacent sequences: A141565 A141566 A141567 this_sequence A141569 A141570 A141571
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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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