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A301591 Primes p that have other solutions x to A023900(x) = A023900(p) than a power of p.

%I A301591 #16 Aug 15 2021 15:29:26
%S A301591 13,37,41,61,73,89,97,109,113,157,181,193,233,241,277,281,313,337,349,
%T A301591 353,397,401,409,421,433,449,457,461,521,541,577,593,601,613,617,641,
%U A301591 661,673,701,733,757,761,769,821,829,877,881,929,937,953,997,1009,1013,1021,1033,1049
%N A301591 Primes p that have other solutions x to A023900(x) = A023900(p) than a power of p.
%C A301591 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
%H A301591 David A. Corneth, <a href="/A301591/b301591.txt">Table of n, a(n) for n = 1..10000</a>
%e A301591 13 is a term because A023900(42) = A023900(13), where 42 is not a power of 13.
%o A301591 (PARI) f(n) = sumdivmult(n, d, d*moebius(d)); /* This is A023900 */
%o A301591 isok(p, vp) = {for (k=p+1, p^2-1, if (f(k) == vp, return (0)); ); return (1); }
%o A301591 lista(nn) = {forprime(p=2, nn, vp = f(p); if (!isok(p, vp), print1(p, ", ")); ); }
%Y A301591 Cf. A001055, A023900, A301374.
%Y A301591 Complement of A301590.
%Y A301591 A005383 \ {3,5} is a subsequence.
%K A301591 nonn
%O A301591 1,1
%A A301591 _Michel Marcus_, Mar 24 2018