A371412 Euler totient function applied to the cubefull numbers (A036966).

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

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

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

Cf. A000010, A013661, A036966, A098198.

Similar sequences: A323333, A358039, A371413, A371414.

Sequence in context: A312825 A312826 A110601 * A107926 A174741 A312827

Adjacent sequences: A371409 A371410 A371411 * A371413 A371414 A371415

Keyword

nonn,easy

Author

Amiram Eldar, Mar 22 2024

Status

approved