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A371415
Dedekind psi function applied to the cubefull exponentially odd numbers (A335988).
4
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
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
Similar sequences: A323332, A371413, A371414.
Sequence in context: A349020 A074234 A076515 * A039317 A298942 A322411
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 22 2024
STATUS
approved