A351475 - OEIS

%I #9 Feb 15 2022 20:55:54

%S 1,2,5,5,10,10,17,10,8,20,26,25,37,34,50,17,50,16,65,50,85,52,82,50,

%T 13,74,13,85,101,100,122,26,130,100,170,40,145,130,185,100,170,170,

%U 197,130,80,164,226,85,20,26,250,185,257,26,260,170,325,202,290,250

%N Multiplicative with a(prime(k)^e) = k^2 + e^2 for any k, e > 0.

%C This sequence gives the norm of the function f defined in A351464-A351465.

%F a(n) = A351464(n)^2 + A351465(n)^2.

%e For n = 42:

%e - 42 = 2 * 3 * 7 = prime(1)^1 * prime(2)^1 * prime(4)^1,

%e - a(42) = (1^2 + 1^2) * (2^2 + 1^2) * (4^2 + 1^2) = 170.

%p a:= proc(n) option remember; uses numtheory;

%p       mul(pi(i[1])^2+i[2]^2, i=ifactors(n)[2])

%p     end:

%p seq(a(n), n=1..60);  # _Alois P. Heinz_, Feb 15 2022

%t f[p_, e_] := PrimePi[p]^2 + e^2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 15 2022 *)

%o (PARI) a(n) = { my (f=factor(n), p=f[, 1]~, e=f[, 2]~); prod (k=1, #p, primepi(p[k])^2 + e[k]^2) }

%Y Cf. A351464, A351465, A289320.

%K nonn,mult

%O 1,2

%A _Rémy Sigrist_, Feb 12 2022