A064971 a(n) = n*usigma(n), where usigma(n) is the sum of unitary divisors of n (A034448).

1, 6, 12, 20, 30, 72, 56, 72, 90, 180, 132, 240, 182, 336, 360, 272, 306, 540, 380, 600, 672, 792, 552, 864, 650, 1092, 756, 1120, 870, 2160, 992, 1056, 1584, 1836, 1680, 1800, 1406, 2280, 2184, 2160, 1722, 4032, 1892, 2640, 2700, 3312, 2256

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = p^e*(p^e+1). - Vladeta Jovovic, Nov 01 2001

Dirichlet g.f.: zeta(s-1)*zeta(s-2)/zeta(2*s-3). - R. J. Mathar, Feb 09 2011

Sum_{k=1..n} a(k) ~ Pi^2 * n^3 / (18*Zeta(3)). - Vaclav Kotesovec, Feb 01 2019

Sum_{k>=1} 1/a(k) = Product_{primes p} (3/2 + 1/(p-1) - (log(1-p) + QPolyGamma(1 - i*Pi/log(p), p))/log(p)) = 1.46909915920728851157169314962365889937120909118052326761431400799664418179... - Vaclav Kotesovec, Sep 20 2020

Maple

seq(mul(ifactors(n)[2][i][1]^ifactors(n)[2][i][2]*(1+ifactors(n)[2][i][1]^ifactors(n)[2][i][2]), i=1..nops(ifactors(n)[2])), n=1..50);

Prog

(PARI) usigma(n)= { local(f, s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) } { for (n=1, 1000, write("b064971.txt", n, " ", n*usigma(n)) ) } \\ Harry J. Smith, Oct 01 2009

Crossrefs

Cf. A034448.

Sequence in context: A180291 A056930 A326378 * A130199 A295904 A309836

Adjacent sequences: A064968 A064969 A064970 * A064972 A064973 A064974

Keyword

mult,nonn

Author

N. J. A. Sloane, Oct 30 2001

Status

approved