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

1,3

Links

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

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A285213 A285339 A344931 * A050452 A267875 A200517

Adjacent sequences: A005079 A005080 A005081 * A005083 A005084 A005085

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved