A141229 - OEIS

A141229

Odd numbers k for which A006694((k-1)/2) = 3.

27, 43, 109, 125, 157, 229, 277, 283, 307, 499, 643, 691, 733, 739, 811, 997, 1021, 1051, 1069, 1093, 1331, 1459, 1579, 1597, 1627, 1699, 1723, 1789, 1933, 2179, 2197, 2203, 2251, 2341, 2347, 2749, 2917, 3163, 3181, 3229, 3259, 3373, 4027, 4339, 4549, 4597, 4651, 4909

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OFFSET

1,1

COMMENTS

Conjecture. The terms of the sequence have only one prime divisor; moreover, p^3 is in the sequence if and only if p is in A001122.

LINKS

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

MATHEMATICA

r[n_] := EulerPhi[n]/MultiplicativeOrder[2, n]; Select[Range[5000], Total@(r /@ Divisors[#]) - 1 == 3 &] (* Amiram Eldar, Sep 12 2019 *)

PROG

(PARI) a006694(n)=sumdiv(2*n+1, d, eulerphi(d)/znorder(Mod(2, d))) - 1;

isok(n) = (n % 2) && (a006694((n-1)/2) == 3); \\ Michel Marcus, Feb 08 2016