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A143520
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a(n) is n times number of divisors of n if n is odd, zero if n is twice odd, n times number of divisors of n/4 if n is divisible by 4.
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1
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1, 0, 6, 4, 10, 0, 14, 16, 27, 0, 22, 24, 26, 0, 60, 48, 34, 0, 38, 40, 84, 0, 46, 96, 75, 0, 108, 56, 58, 0, 62, 128, 132, 0, 140, 108, 74, 0, 156, 160, 82, 0, 86, 88, 270, 0, 94, 288, 147, 0, 204, 104, 106, 0, 220, 224, 228, 0, 118, 240, 122, 0, 378, 320, 260, 0, 134, 136
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(n) is multiplicative with a(2^e) = (e-1) * 2^e if e>0, a(p^e) = (e+1) * p^e if p>2.
a(4*n + 2) = 0.
G.f.: Sum_{k>0} k * x^k / (1 - (-x)^k)^2.
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EXAMPLE
| q + 6*q^3 + 4*q^4 + 10*q^5 + 14*q^7 + 16*q^8 + 27*q^9 + 22*q^11 + 24*q^12 + ...
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PROG
| (PARI) {a(n) = local(A, p, e); if( n<1, 0, A = factor(n); prod(k=1, matsize(A)[1], if(p = A[k, 1], e = A[k, 2]; (e - (-1)^p) * p^e)))}
(PARI) {a(n) = if( n<1, 0, polcoeff( sum(k=1, n, k * x^k / (1 - (-x)^k)^2, x*O(x^n)), n))}
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CROSSREFS
| A038040(2*n + 1) = a(2*n + 1). 4 * A038040(n) = a(4*n).
Sequence in context: A168198 A177898 A082209 * A075450 A145979 A015906
Adjacent sequences: A143517 A143518 A143519 * A143521 A143522 A143523
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Aug 22 2008
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