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Search: id:A074854
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| A074854 |
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a(n)=Sum(d|n)(2^(n-d)). |
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+0
5
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| 1, 3, 5, 13, 17, 57, 65, 209, 321, 801, 1025, 3905, 4097, 9407, 21505, 53505, 65537, 233985, 262145, 885761, 1327105, 3147777, 4194305, 16060417, 17825793, 50339841, 84148225, 220217345, 268435457, 990937089, 1073741825, 3506503681
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A034729=Sum(d|n)(2^(d-1)) A055895=2*A034729 If p is a prime, then a(p)=A034729(p)=2^(p-1)+1
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FORMULA
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G.f.: 2^n times coefficient of x^n in sum(k>=1, 2/(2-x^k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
G.f.: Sum_{k>0} 2^(k-1)*x^k/(1-2^(k-1)*x^k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 24 2003
Triangle A051731 mod 2 converted to decimal. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Oct 04 2003
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EXAMPLE
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Divisors of 6 = 1,2,3,6, and 6-1=5, 6-2=4, 6-3=3, 6-6=0. a(6)=2^5+2^4+2^3+2^0=32+16+8+1=57
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 2^n*polcoeff(sum(k=1, n, 2/(2-x^k), x*O(x^n)), n))
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CROSSREFS
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Cf. A055895, A034729.
Cf. A080267.
Cf. A051731.
Sequence in context: A089996 A080076 A128339 this_sequence A038185 A131020 A084706
Adjacent sequences: A074851 A074852 A074853 this_sequence A074855 A074856 A074857
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KEYWORD
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easy,nonn
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AUTHOR
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M. Kristof (kristmikl(AT)freemail.hu), Sep 11 2002
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