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

1,1

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.

Sequence in context: A264908 A281004 A088963 * A301857 A220462 A280997

Adjacent sequences: A301588 A301589 A301590 * A301592 A301593 A301594

Keyword

nonn

Author

Michel Marcus, Mar 24 2018

Status

approved