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

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)

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

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

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

Extensions

More terms from Antti Karttunen, Jul 11 2017