A005068 Sum of 4th powers of odd primes dividing n.

0, 0, 81, 0, 625, 81, 2401, 0, 81, 625, 14641, 81, 28561, 2401, 706, 0, 83521, 81, 130321, 625, 2482, 14641, 279841, 81, 625, 28561, 81, 2401, 707281, 706, 923521, 0, 14722, 83521, 3026, 81, 1874161, 130321, 28642, 625, 2825761, 2482, 3418801, 14641, 706, 279841, 4879681, 81, 2401, 625, 83602, 28561, 7890481, 81

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

Additive with a(p^e) = 0 if p = 2, p^4 otherwise.

From Antti Karttunen, Jul 10 2017: (Start)

a(1) = 0; after which, for even n: a(n) = a(n/2), for odd n: a(n) = A020639(n)^4 + a(A028234(n)).

a(n) = A005065(A000265(n)).

(End)

G.f.: Sum_{k>=2} prime(k)^4 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Aug 19 2021

Mathematica

Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, OddQ@ #] &] &, 54] (* Michael De Vlieger, Jul 11 2017 *)
f[2, e_] := 0; f[p_, e_] := p^4; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 50] (* Amiram Eldar, Jun 20 2022 *)

Prog

(Scheme) (define (A005068 n) (cond ((= 1 n) 0) ((even? n) (A005068 (/ n 2))) (else (+ (A000583 (A020639 n)) (A005068 (A028234 n)))))) ;; Antti Karttunen, Jul 10 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%2) == 1, p^4)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000265, A000583, A005065, A005066, A005067, A005069, A020639, A028234.

Sequence in context: A005085 A050455 A110727 * A366458 A259687 A065793

Adjacent sequences: A005065 A005066 A005067 * A005069 A005070 A005071

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 10 2017

Status

approved