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A202994 a(n) = sigma(n^4). 5
1, 31, 121, 511, 781, 3751, 2801, 8191, 9841, 24211, 16105, 61831, 30941, 86831, 94501, 131071, 88741, 305071, 137561, 399091, 338921, 499255, 292561, 991111, 488281, 959171, 797161, 1431311, 732541, 2929531, 954305, 2097151, 1948705, 2750971, 2187581 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Here sigma(n^4) denotes the sums of divisors of n^4.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(11*n) == 0 (mod 5) iff gcd(n,11) = 1.

Logarithmic derivative of A202993.

Multiplicative with a(p^e) = (p^(4*e+1)-1)/(p-1) for prime p. - Andrew Howroyd, Jul 23 2018

EXAMPLE

L.g.f.: L(x) = x + 31*x^2/2 + 121*x^3/3 + 511*x^4/4 + 781*x^5/5 + 3751*x^6/6 +...

where exp(L(x)) = 1 + x + 16*x^2 + 56*x^3 + 296*x^4 + 1052*x^5 + 4952*x^6 +...+ A202993(n)*x^n +...

MATHEMATICA

DivisorSigma[1, Range[40]^4] (* Harvey P. Dale, Jan 29 2012 *)

PROG

(PARI) {a(n)=sigma(n^4)}

CROSSREFS

Cf. A000203 (sigma), A065764, A175926, A202993.

Sequence in context: A131550 A158558 A160893 * A038992 A068021 A131992

Adjacent sequences:  A202991 A202992 A202993 * A202995 A202996 A202997

KEYWORD

nonn,mult

AUTHOR

Paul D. Hanna, Dec 27 2011

EXTENSIONS

Keyword:mult added by Andrew Howroyd, Jul 23 2018

STATUS

approved

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Last modified May 21 01:01 EDT 2019. Contains 323429 sequences. (Running on oeis4.)