A344971 a(n) = A344875(n) / gcd(A011772(n), A344875(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 7, 1, 18, 8, 1, 1, 3, 1, 28, 2, 30, 1, 2, 1, 3, 1, 6, 1, 8, 1, 1, 20, 3, 12, 7, 1, 54, 2, 4, 1, 9, 1, 35, 32, 66, 1, 31, 1, 3, 32, 28, 1, 26, 4, 15, 2, 3, 1, 56, 1, 90, 16, 1, 48, 60, 1, 7, 44, 18, 1, 40, 1, 3, 2, 9, 20, 6, 1, 31, 1, 3, 1, 7, 32, 126, 56, 75, 1, 96, 72, 154, 2, 138, 72

Offset: 1

Author

Antti Karttunen, Jun 04 2021

Keywords

• nonn
• frac

Comments

Numerator of the ratio A344875(n)/A011772(n): 1/1, 3/3, 2/2, 7/7, 4/4, 6/3, 6/6, 15/15, 8/8, 12/4, 10/10, 14/8, 12/12, 18/7, 8/5, 31/31, 16/16, 24/8, 18/18, 28/15, 12/6, 30/11, ... = 1/1, 1/1, 1/1, 1/1, 1/1, 2/1, 1/1, 1/1, 1/1, 3/1, 1/1, 7/4, 1/1, 18/7, 8/5, 1/1, 1/1, 3/1, 1/1, 28/15, 2/1, 30/11, etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A011772, A344875, A344969, A344970 (denominators), A344972 (ratio A344875/A011772 floored down), A344973 (and their remainder).

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)); };
A344971(n) = { my(u=A344875(n)); (u/gcd(u, A011772(n))); };

Formula

a(n) = A344875(n) / A344969(n) = A344875(n) / gcd(A011772(n), A344875(n)).