A224903 - OEIS

A224903

a(n) = sigma(2*n^4) - sigma(n^4).

2, 32, 242, 512, 1562, 3872, 5602, 8192, 19682, 24992, 32210, 61952, 61882, 89632, 189002, 131072, 177482, 314912, 275122, 399872, 677842, 515360, 585122, 991232, 976562, 990112, 1594322, 1434112, 1465082, 3024032, 1908610, 2097152, 3897410, 2839712, 4375162, 5038592, 3852442

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OFFSET

1,1

COMMENTS

Here sigma(n) = A000203(n), the sum of the divisors of n.

LINKS

Table of n, a(n) for n=1..37.

FORMULA

a(n) = A054785(n^4).

Logarithmic derivative of A224902.

Sum_{k=1..n} a(k) ~ c * n^5, where c = (31/115) * zeta(5) * Product_{p prime} (1 + 1/p^2 + 1/p^3 + 1/p^5) = 0.51764417195990550114... . - Amiram Eldar, Mar 17 2024

EXAMPLE

L.g.f.: L(x) = 2*x + 32*x^2/2 + 242*x^3/3 + 512*x^4/4 + 1562*x^5/5 +...

where exponentiation yields the g.f. of A224902:

exp(L(x)) = 1 + 2*x + 18*x^2 + 114*x^3 + 450*x^4 + 2298*x^5 +...

MATHEMATICA

a[n_] := DivisorSigma[1, 2*n^4] - DivisorSigma[1, n^4]; Array[a, 50] (* Amiram Eldar, Mar 17 2024 *)

PROG

(PARI) {a(n)=sigma(2*n^4)-sigma(n^4)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Cf. A224902, A054785, A000203, A013663.

Sequence in context: A053316 A053053 A053054 * A008512 A179074 A035602

Adjacent sequences: A224900 A224901 A224902 * A224904 A224905 A224906

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 24 2013

STATUS

approved