A005082 Sum of primes = 3 mod 4 dividing n.

0, 0, 3, 0, 0, 3, 7, 0, 3, 0, 11, 3, 0, 7, 3, 0, 0, 3, 19, 0, 10, 11, 23, 3, 0, 0, 3, 7, 0, 3, 31, 0, 14, 0, 7, 3, 0, 19, 3, 0, 0, 10, 43, 11, 3, 23, 47, 3, 7, 0, 3, 0, 0, 3, 11, 7, 22, 0, 59, 3, 0, 31, 10, 0, 0, 14, 67, 0, 26, 7, 71, 3, 0, 0, 3, 19, 18, 3, 79, 0, 3, 0, 83, 10, 0, 43, 3, 11, 0, 3, 7, 23, 34, 47, 19, 3, 0, 7, 14, 0, 0, 3, 103

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A005069, A005078, A005083, A005084, A005085, A008472, A059841.

Programs

Mathematica

Table[Total[Select[Transpose[FactorInteger[n]][[1]],Mod[#,4] == 3&]],{n,80}] (* Harvey P. Dale, Jan 18 2015 *)
Array[DivisorSum[#, # &, And[PrimeQ@ #, Mod[#, 4] == 3] &] &, 103] (* Michael De Vlieger, Jul 11 2017 *)

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k,1])%4) == 3, p)); \\ Michel Marcus, Jul 11 2017

Scheme

(define (A005082 n) (if (= 1 n) 0 (+ (* (A079978 (modulo (A020639 n) 4)) (A020639 n)) (A005082 (A028234 n))))) ;; Antti Karttunen, Jul 11 2017

Formula

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

From Antti Karttunen, Jul 11 2017: (Start)

a(1) = 0; for n > 1, a(n) = (A079978(A020639(n) mod 4)*A020639(n)) + a(A028234(n)).

a(n) = A008472(n) - A005078(n) - 2*A059841(n).

(End)

Extensions

More terms from Antti Karttunen, Jul 11 2017