A005077 Sum of 4th powers of primes = 2 mod 3 dividing n.

0, 16, 0, 16, 625, 16, 0, 16, 0, 641, 14641, 16, 0, 16, 625, 16, 83521, 16, 0, 641, 0, 14657, 279841, 16, 625, 16, 0, 16, 707281, 641, 0, 16, 14641, 83537, 625, 16, 0, 16, 0, 641, 2825761, 16, 0, 14657, 625, 279857, 4879681, 16, 0, 641, 83521, 16, 7890481, 16, 15266, 16, 0, 707297, 12117361, 641, 0, 16, 0, 16, 625, 14657, 0, 83537

Offset

1,2

Links

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

Formula

Additive with a(p^e) = p^4 if p = 2 (mod 3), 0 otherwise.

a(n) = A005065(n) - A005073(n) - 81*A079978(n). - Antti Karttunen, Jul 10 2017

Mathematica

Array[DivisorSum[#, #^4 &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 68] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 3] == 2, p^4, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005077 n) (if (= 1 n) 0 (+ (A000583 (if (= 2 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005077 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%3) == 2, p^4)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000583, A005065, A005073, A005074, A005075, A005076, A008472, A079978.

Sequence in context: A070570 A347158 A347160 * A059060 A331140 A059681

Adjacent sequences: A005074 A005075 A005076 * A005078 A005079 A005080

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 10 2017

Status

approved