A005075 Sum of squares of primes = 2 mod 3 dividing n.

0, 4, 0, 4, 25, 4, 0, 4, 0, 29, 121, 4, 0, 4, 25, 4, 289, 4, 0, 29, 0, 125, 529, 4, 25, 4, 0, 4, 841, 29, 0, 4, 121, 293, 25, 4, 0, 4, 0, 29, 1681, 4, 0, 125, 25, 533, 2209, 4, 0, 29, 289, 4, 2809, 4, 146, 4, 0, 845, 3481, 29, 0, 4, 0, 4, 25, 125, 0, 293, 529, 29, 5041, 4, 0, 4, 25, 4, 121, 4, 0, 29, 0, 1685, 6889, 4, 314

Offset

1,2

Links

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

Formula

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

a(n) = A005063(n) - A005071(n) - 9*A079978(n). - Antti Karttunen, Jul 10 2017

Mathematica

Array[DivisorSum[#, #^2 &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 85] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 3] == 2, p^2, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(Scheme) (define (A005075 n) (if (= 1 n) 0 (+ (A000290 (if (= 2 (modulo (A020639 n) 3)) (A020639 n) 0)) (A005075 (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^2)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000290, A005063, A005071, A005074, A005076, A005077, A008472, A079978.

Sequence in context: A058493 A112149 A087736 * A103638 A129821 A126836

Adjacent sequences: A005072 A005073 A005074 * A005076 A005077 A005078

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 10 2017

Status

approved