A005081 Sum of 4th powers of primes = 1 mod 4 dividing n.

0, 0, 0, 0, 625, 0, 0, 0, 0, 625, 0, 0, 28561, 0, 625, 0, 83521, 0, 0, 625, 0, 0, 0, 0, 625, 28561, 0, 0, 707281, 625, 0, 0, 0, 83521, 625, 0, 1874161, 0, 28561, 625, 2825761, 0, 0, 0, 625, 0, 0, 0, 0, 625, 83521, 28561, 7890481, 0, 625, 0, 0, 707281, 0, 625, 13845841, 0, 0, 0, 29186, 0, 0, 83521, 0, 625, 0, 0, 28398241

Offset

1,5

Links

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

Formula

Additive with a(p^e) = p^4 if p = 1 (mod 4), 0 otherwise.

a(n) = A005065(n) - A005085(n) - 16*A059841(n). - Antti Karttunen, Jul 11 2017

Mathematica

Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 73] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 1, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005081 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A000583 (A020639 n)) 0) (A005081 (A028234 n))))) ;; Antti Karttunen, Jul 11 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%4) == 1, p^4)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000583, A005065, A005078, A005079, A005080, A005085, A059841.

Sequence in context: A223215 A057012 A115484 * A210115 A186484 A184037

Adjacent sequences: A005078 A005079 A005080 * A005082 A005083 A005084

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved