A005078 Sum of primes = 1 mod 4 dividing n.

0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 13, 0, 5, 0, 17, 0, 0, 5, 0, 0, 0, 0, 5, 13, 0, 0, 29, 5, 0, 0, 0, 17, 5, 0, 37, 0, 13, 5, 41, 0, 0, 0, 5, 0, 0, 0, 0, 5, 17, 13, 53, 0, 5, 0, 0, 29, 0, 5, 61, 0, 0, 0, 18, 0, 0, 17, 0, 5, 0, 0, 73, 37, 5, 0, 0, 13, 0, 5, 0, 41, 0, 0, 22, 0, 29, 0, 89, 5, 13, 0, 0, 0, 5, 0, 97, 0, 0, 5, 101

Offset

1,5

Links

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

Formula

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

a(n) = A008472(n) - A005082(n) - 2*A059841(n). - Antti Karttunen, Jul 11 2017

Mathematica

Array[DivisorSum[#, # &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 101] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 1, p, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(PARI) a(n)=my(f=factor(n)[, 1]); sum(i=1, #f, if(f[i]%4==1, f[i])) \\ Charles R Greathouse IV, Mar 11 2014
(Scheme) (define (A005078 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A020639 n) 0) (A005078 (A028234 n))))) ;; Antti Karttunen, Jul 11 2017

Crossrefs

Cf. A005069, A005079, A005080, A005081, A005082, A008472, A059841.

Sequence in context: A336881 A369449 A324323 * A284446 A270030 A284104

Adjacent sequences: A005075 A005076 A005077 * A005079 A005080 A005081

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 11 2017

Status

approved