A005079 Sum of squares of primes = 1 mod 4 dividing n.

0, 0, 0, 0, 25, 0, 0, 0, 0, 25, 0, 0, 169, 0, 25, 0, 289, 0, 0, 25, 0, 0, 0, 0, 25, 169, 0, 0, 841, 25, 0, 0, 0, 289, 25, 0, 1369, 0, 169, 25, 1681, 0, 0, 0, 25, 0, 0, 0, 0, 25, 289, 169, 2809, 0, 25, 0, 0, 841, 0, 25, 3721, 0, 0, 0, 194, 0, 0, 289, 0, 25, 0, 0, 5329, 1369, 25, 0, 0, 169, 0, 25, 0, 1681, 0, 0, 314

Offset

1,5

Links

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

Formula

Additive with a(p^e) = p^2 if p = 1 (mod 4), 0 otherwise.

a(n) = A005063(n) - A005083(n) - 4*A059841(n). - Antti Karttunen, Jul 11 2017

Mathematica

Array[DivisorSum[#, #^2 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 85] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 1, p^2, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005079 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A000290 (A020639 n)) 0) (A005079 (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^2)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000290, A005063, A005078, A005080, A005081, A005083, A059841.

Sequence in context: A067669 A068741 A255403 * A167624 A181614 A108321

Adjacent sequences: A005076 A005077 A005078 * A005080 A005081 A005082

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved