A344979 Numbers k such that A011772(k) is equal to A344878(k).

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 26, 27, 29, 31, 32, 37, 39, 41, 43, 47, 49, 50, 53, 57, 59, 61, 64, 67, 71, 73, 74, 75, 78, 79, 81, 83, 89, 93, 97, 98, 101, 103, 107, 109, 111, 113, 121, 122, 125, 127, 128, 129, 131, 137, 139, 146, 147, 149, 150, 151, 157, 163, 167, 169, 173, 179, 181, 183, 191, 193, 194

Offset: 1

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn

Crossrefs

Cf. A011772, A344878, A344885 (characteristic function).

Positions of zeros in A344976.

Union of A000961 and A344978. Subsequence of A344974.

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
A344878(n) = if(1==n,n, my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^(f[2, i]+(2==f[1, i]))-1))));
isA344979(n) = (A344878(n)==A011772(n));