A291524 Numbers m such that psi(x) = phi(m) has a solution while sigma(y) = phi(m) has none.

751, 919, 1502, 1838, 2841, 3788, 5682, 6629, 8523, 11251, 11937, 13258, 13669, 14205, 15137, 15152, 15397, 15607, 15916, 16099, 17046, 18940, 19895, 22502, 22728, 23874, 27338, 28410, 30103, 30274, 30304, 30794, 31214, 31832, 32198, 36853, 37880, 39790, 43657

Offset: 1

Author

Altug Alkan, Aug 25 2017

Keywords

• nonn

Comments

Values of A069825(k) such that psi(x) = phi(A069825(k)) has a solution for k > 1.

Prime terms are 751, 919, 11251, 13669, 15137, ...

Examples

			751 is a term because psi(x) = phi(751) = 750 has a solution that is x = 625 while there is no solution for sigma(y) = phi(751) = 750.
		

Crossrefs

Cf. A000010, A000203, A001615, A069825.

Programs

PARI

is1(n) = my(N=eulerphi(n)); for(k=1, N, if(sigma(k)==N, return(1))); 0;
a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));
is2(n) = my(N=eulerphi(n)); for(k=1, N, if(a001615(k)==N, return(1))); 0;
isok(n) = !is1(n) && is2(n); \\ after Charles R Greathouse IV at A001615