A005085 Sum of 4th powers of primes = 3 mod 4 dividing n.

0, 0, 81, 0, 0, 81, 2401, 0, 81, 0, 14641, 81, 0, 2401, 81, 0, 0, 81, 130321, 0, 2482, 14641, 279841, 81, 0, 0, 81, 2401, 0, 81, 923521, 0, 14722, 0, 2401, 81, 0, 130321, 81, 0, 0, 2482, 3418801, 14641, 81, 279841, 4879681, 81, 2401, 0, 81, 0, 0, 81, 14641, 2401, 130402, 0, 12117361, 81, 0, 923521, 2482, 0, 0, 14722, 20151121, 0, 279922

Offset

1,3

Links

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

Formula

Additive with a(p^e) = p^4 if p = 3 (mod 4), 0 otherwise.

a(n) = A005065(n) - A005081(n) - 16*A059841(n). - Antti Karttunen, Jul 11 2017

Mathematica

Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 4] == 3] &] &, 69] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 3, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005085 n) (if (= 1 n) 0 (+ (if (= 3 (modulo (A020639 n) 4)) (A000583 (A020639 n)) 0) (A005085 (A028234 n))))) ;; Antti Karttunen, Jul 11 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%4) == 3, p^4)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000583, A005065, A005081, A005082, A005083, A005084, A059841.

Sequence in context: A208187 A116230 A056669 * A050455 A110727 A005068

Adjacent sequences: A005082 A005083 A005084 * A005086 A005087 A005088

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved