A344972 a(n) = floor(A344875(n) / A011772(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 2, 1, 3, 1, 6, 1, 1, 1, 1, 1, 3, 1, 7, 1, 2, 2, 4, 1, 1, 1, 2, 3, 2, 1, 1, 1, 3, 1, 2, 1, 2, 4, 1, 2, 3, 1, 3, 1, 2, 1, 1, 1, 5, 1, 7, 1, 3, 1, 1, 1, 3, 2, 2, 2, 6, 1, 1, 1, 3, 1, 1, 1, 2, 1, 4, 1, 2, 5, 6, 2, 2, 3, 2, 1, 3, 1, 7, 1, 1, 1, 2, 3

Offset: 1

Author

Antti Karttunen, Jun 04 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A011772, A344875, A344876, A344969, A344970, A344971, A344973.

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)); };
A344972(n) = floor(A344875(n)/A011772(n));

Formula

a(n) = (A344875(n)-A344973(n)) / A011772(n) = floor(A344875(n) / A011772(n)).

a(n) = floor(A344971(n) / A344970(n)). - Antti Karttunen, Jun 20 2021