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

Offset: 1

Author

Michel Marcus, Mar 24 2018

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A001055, A023900, A301374.

Complement of A301590.

A005383 \ {3,5} is a subsequence.

Programs

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, ", ")); ); }