A339875 - OEIS

%I #7 Dec 28 2020 09:51:29

%S 561,6601,8481,17733,23001,30889,54741,62745,88561,106141,319965,

%T 359601,449065,534061,609301,949785,1357621,2162721,2288661,2615977,

%U 3284281,4005001,4698001,4830805,5381265,6313681,6594721,6840001,8093701,11782005,11921001,14665105,14892153,15217741,16577785,19683001,20154061,20441701

%N 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.

%C 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.

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

%o (PARI)

%o A065338(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = (f[i, 1]%4)); factorback(f); };

%o isA137409(n) = ((1==n)||(A065338(n)>1)); \\ _Antti Karttunen_, Dec 26 2020

%o A000265(n) = (n>>valuation(n, 2));

%o isA339870(n) = ((n>1)&&!isprime(n)&&(1==(n%4))&&!((n-1)%A000265(eulerphi(n))));

%o isA339875(n) = (isA137409(n)&&isA339870(n));

%Y Intersection of A137409 and A339870.

%Y Cf. A000010, A000265, A053575, A065338.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 26 2020