A380324 The sum of the squares dividing the n-th exponentially odd number.

1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 10, 1, 1, 1, 21, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 10, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 21, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5

Offset: 1

Author

Amiram Eldar, Jan 20 2025

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A035316, A268335, A380323, A380325.

Programs

Mathematica

f[p_, e_] := If[OddQ[e], (p^(e+1) - 1)/(p^2 - 1), 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &]

PARI

s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] % 2, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1]^2 - 1), 0));}
list(lim) = select(x -> x > 0, vector(lim, i, s(i)));

Formula

a(n) = A035316(A268335(n)).