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A005080
Sum of cubes of primes = 1 mod 4 dividing n.
6
0, 0, 0, 0, 125, 0, 0, 0, 0, 125, 0, 0, 2197, 0, 125, 0, 4913, 0, 0, 125, 0, 0, 0, 0, 125, 2197, 0, 0, 24389, 125, 0, 0, 0, 4913, 125, 0, 50653, 0, 2197, 125, 68921, 0, 0, 0, 125, 0, 0, 0, 0, 125, 4913, 2197, 148877, 0, 125, 0, 0, 24389, 0, 125, 226981, 0, 0, 0, 2322, 0, 0, 4913, 0, 125, 0, 0, 389017, 50653, 125
OFFSET
1,5
LINKS
FORMULA
Additive with a(p^e) = p^3 if p = 1 (mod 4), 0 otherwise.
a(n) = A005064(n) - A005084(n) - 8*A059841(n). - Antti Karttunen, Jul 11 2017
MATHEMATICA
Array[DivisorSum[#, #^3 &, And[PrimeQ@ #, Mod[#, 4] == 1] &] &, 75] (* Michael De Vlieger, Jul 11 2017 *)
f[p_, e_] := If[Mod[p, 4] == 1, p^3, 0]; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)
PROG
(Scheme) (define (A005080 n) (if (= 1 n) 0 (+ (if (= 1 (modulo (A020639 n) 4)) (A000578 (A020639 n)) 0) (A005080 (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^3)); \\ Michel Marcus, Jul 11 2017
KEYWORD
nonn
EXTENSIONS
More terms from Antti Karttunen, Jul 11 2017
STATUS
approved