A344980 Numbers k such that A011772(k) does not divide A344875(k).

12, 14, 15, 20, 22, 30, 33, 35, 38, 42, 44, 45, 46, 48, 51, 52, 54, 56, 60, 62, 63, 65, 66, 69, 70, 72, 76, 77, 80, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 99, 102, 104, 105, 108, 110, 112, 114, 115, 116, 117, 118, 119, 123, 124, 126, 130, 132, 133, 134, 135, 138, 140, 141, 142, 143, 144, 145, 148, 152, 153, 154, 156

Offset: 1

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn

Comments

The first term not in A344883 is 60. First terms included in A344883, but not here are: 900, 1260, 1560, 3740, 6552, 6669, etc. (A344694). See also comments in A344975.

Crossrefs

Cf. A011772, A344694, A344875, A344975.

Complement of A344974. Positions of nonzero terms in A344973, and of terms > 1 in A344970.

Programs

PARI

A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
isA344980(n) = (A344875(n)%A011772(n));