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A351475 Multiplicative with a(prime(k)^e) = k^2 + e^2 for any k, e > 0.

%I A351475 #9 Feb 15 2022 20:55:54
%S A351475 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 A351475 13,74,13,85,101,100,122,26,130,100,170,40,145,130,185,100,170,170,
%U A351475 197,130,80,164,226,85,20,26,250,185,257,26,260,170,325,202,290,250
%N A351475 Multiplicative with a(prime(k)^e) = k^2 + e^2 for any k, e > 0.
%C A351475 This sequence gives the norm of the function f defined in A351464-A351465.
%F A351475 a(n) = A351464(n)^2 + A351465(n)^2.
%e A351475 For n = 42:
%e A351475 - 42 = 2 * 3 * 7 = prime(1)^1 * prime(2)^1 * prime(4)^1,
%e A351475 - a(42) = (1^2 + 1^2) * (2^2 + 1^2) * (4^2 + 1^2) = 170.
%p A351475 a:= proc(n) option remember; uses numtheory;
%p A351475       mul(pi(i[1])^2+i[2]^2, i=ifactors(n)[2])
%p A351475     end:
%p A351475 seq(a(n), n=1..60);  # _Alois P. Heinz_, Feb 15 2022
%t A351475 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 A351475 (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 A351475 Cf. A351464, A351465, A289320.
%K A351475 nonn,mult
%O A351475 1,2
%A A351475 _Rémy Sigrist_, Feb 12 2022