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A371412
Euler totient function applied to the cubefull numbers (A036966).
2
1, 4, 8, 18, 16, 32, 54, 100, 64, 72, 162, 128, 294, 144, 256, 500, 216, 486, 288, 400, 512, 432, 1210, 576, 648, 800, 1024, 1458, 2028, 2058, 864, 1176, 2500, 1800, 1152, 1296, 1600, 2048, 4624, 2000, 1728, 2352, 1944, 4374, 6498, 2304, 2592, 3200, 4096, 5292, 4000
OFFSET
1,2
LINKS
FORMULA
a(n) = A000010(A036966(n)).
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/((p-1)^2*p)) = zeta(2)^2 * Product_{p prime} (1 - 2/p^2 + 1/p^3 + 3/p^4 + 1/p^5) = 1.65532418864085918623... .
MATHEMATICA
Join[{1}, EulerPhi /@ Select[Range[20000], AllTrue[Last /@ FactorInteger[#], #1 > 2 &] &]]
(* or *)
f[n_] := Module[{f = FactorInteger[n], p, e}, If[n == 1, 1, p = f[[;; , 1]]; e = f[[;; , 2]]; If[Min[e] > 2, Times @@ ((p-1) * p^(e-1)), Nothing]]]; Array[f, 20000]
PROG
(PARI) lista(max) = {my(f); print1(1, ", "); for(k = 2, max, f = factor(k); if(vecmin(f[, 2]) > 2, print1(eulerphi(f), ", "))); }
CROSSREFS
Similar sequences: A323333, A358039, A371413, A371414.
Sequence in context: A312825 A312826 A110601 * A107926 A174741 A312827
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 22 2024
STATUS
approved