A339875 Intersection of A137409 and A339870: Composite numbers k of the form 4u+1 having more than one prime factor of type 4u+3, and for which the odd part of phi(k) divides k-1.

561, 6601, 8481, 17733, 23001, 30889, 54741, 62745, 88561, 106141, 319965, 359601, 449065, 534061, 609301, 949785, 1357621, 2162721, 2288661, 2615977, 3284281, 4005001, 4698001, 4830805, 5381265, 6313681, 6594721, 6840001, 8093701, 11782005, 11921001, 14665105, 14892153, 15217741, 16577785, 19683001, 20154061, 20441701

Offset: 1

Author

Antti Karttunen, Dec 26 2020

Keywords

• nonn

Comments

Composite numbers k of the form 4u+1 for which the odd part of phi(k) divides k-1 and for which A065338(k) > 1.

All terms k are squarefree and the 3-adic valuation of A065338(k) is a nonzero even number.

Crossrefs

Intersection of A137409 and A339870.

Cf. A000010, A000265, A053575, A065338.

Programs

PARI

A065338(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = (f[i, 1]%4)); factorback(f); };
isA137409(n) = ((1==n)||(A065338(n)>1)); \\ Antti Karttunen, Dec 26 2020
A000265(n) = (n>>valuation(n, 2));
isA339870(n) = ((n>1)&&!isprime(n)&&(1==(n%4))&&!((n-1)%A000265(eulerphi(n))));
isA339875(n) = (isA137409(n)&&isA339870(n));