A301591 - OEIS

A301591

Primes p that have other solutions x to A023900(x) = A023900(p) than a power of p.

13, 37, 41, 61, 73, 89, 97, 109, 113, 157, 181, 193, 233, 241, 277, 281, 313, 337, 349, 353, 397, 401, 409, 421, 433, 449, 457, 461, 521, 541, 577, 593, 601, 613, 617, 641, 661, 673, 701, 733, 757, 761, 769, 821, 829, 877, 881, 929, 937, 953, 997, 1009, 1013, 1021, 1033, 1049

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OFFSET

1,1

COMMENTS

Contains A005383 \ {3, 5} as a subsequence, since if (p+1)/2 = q > 3 is prime, then A023900(2*3*q) = (1-2)*(1-3)*(1-q) = 1-p = A023900(p). - M. F. Hasler, Aug 14 2021

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

13 is a term because A023900(42) = A023900(13), where 42 is not a power of 13.

PROG

(PARI) f(n) = sumdivmult(n, d, d*moebius(d)); /* This is A023900 */

isok(p, vp) = {for (k=p+1, p^2-1, if (f(k) == vp, return (0)); ); return (1); }

lista(nn) = {forprime(p=2, nn, vp = f(p); if (!isok(p, vp), print1(p, ", ")); ); }

CROSSREFS

Cf. A001055, A023900, A301374.

Complement of A301590.

A005383 \ {3,5} is a subsequence.