A371415 - OEIS

%I #8 Mar 22 2024 17:23:23

%S 1,12,36,48,150,192,432,324,392,768,1728,1800,1452,3888,3072,2916,

%T 2366,4704,3750,5400,6912,7200,5202,7220,15552,12288,14112,17424,

%U 18816,12696,27648,28800,19208,34992,28392,26244,25230,45000,64800,30752,48600,62208,49152

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

%H Amiram Eldar, <a href="/A371415/b371415.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t 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] &] &]]

%o (PARI) dedpsi(f) = prod(i = 1, #f~, (f[i, 1] + 1) * f[i, 1]^(f[i, 2]-1));

%o 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), ", ")));}

%Y Cf. A001615, A065464, A098198, A335988.

%Y Similar sequences: A323332, A371413, A371414.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Mar 22 2024