A371415 Dedekind psi function applied to the cubefull exponentially odd numbers (A335988).

1, 12, 36, 48, 150, 192, 432, 324, 392, 768, 1728, 1800, 1452, 3888, 3072, 2916, 2366, 4704, 3750, 5400, 6912, 7200, 5202, 7220, 15552, 12288, 14112, 17424, 18816, 12696, 27648, 28800, 19208, 34992, 28392, 26244, 25230, 45000, 64800, 30752, 48600, 62208, 49152

Offset

1,2

Links

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

Formula

a(n) = A001615(A335988(n)).

Sum_{n>=1} 1/a(n) = (Pi^4/36) * Product_{p prime} (1 - (2*p-1)/p^3) = A098198 * A065464 = 1.158760974549073218921828... .

Mathematica

psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Join[{1}, psi /@ Select[Range[40000], AllTrue[Last /@ FactorInteger[#], #1 > 1 && OddQ[#1] &] &]]

Prog

(PARI) dedpsi(f) = prod(i = 1, #f~, (f[i, 1] + 1) * f[i, 1]^(f[i, 2]-1));
lista(max) = {my(f, ans); print1(1, ", "); for(k = 2, max, f = factor(k); ans = 1; for (i = 1, #f~, if (f[i, 2] == 1 || !(f[i, 2] % 2), ans = 0; break)); if(ans, print1(dedpsi(f), ", "))); }

Crossrefs

Cf. A001615, A065464, A098198, A335988.

Similar sequences: A323332, A371413, A371414.

Sequence in context: A349020 A074234 A076515 * A039317 A298942 A322411

Adjacent sequences: A371412 A371413 A371414 * A371416 A371417 A371418

Keyword

nonn,easy

Author

Amiram Eldar, Mar 22 2024

Status

approved