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

1,7

Links

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

Formula

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

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 &]

Prog

(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)));

Crossrefs

Cf. A035316, A268335, A380323, A380325.

Sequence in context: A059592 A295554 A319099 * A098087 A354987 A361793

Adjacent sequences: A380321 A380322 A380323 * A380325 A380326 A380327

Keyword

nonn,easy

Author

Amiram Eldar, Jan 20 2025

Status

approved