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

1, 3, 2, 7, 4, 3, 6, 15, 8, 4, 10, 2, 12, 1, 1, 31, 16, 8, 18, 1, 6, 1, 22, 15, 24, 12, 26, 7, 28, 3, 30, 63, 1, 16, 2, 8, 36, 1, 12, 15, 40, 4, 42, 2, 1, 1, 46, 2, 48, 24, 1, 3, 52, 3, 10, 6, 18, 28, 58, 1, 60, 1, 3, 127, 1, 1, 66, 16, 1, 4, 70, 3, 72, 36, 24, 14, 3, 12, 78, 4, 80, 40, 82, 12, 2, 1, 1, 2, 88, 1, 1, 1, 30

Offset: 1

Author

Antti Karttunen, Jun 03 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011772, A344875, A344876, A344970, A344971, A344972, A344973.

Programs

Mathematica

A011772[n_] := Module[{m = 1}, While[Not[IntegerQ[m(m+1)/(2n)]], m++]; m];
A344875[n_] := Product[{p, e} = pe; If[p == 2, 2^(1+e)-1, p^e-1], {pe, FactorInteger[n]}];
a[n_] := GCD[A011772[n], A344875[n]];
Array[a, 100] (* Jean-François Alcover, Jun 12 2021 *)

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)); };
A344969(n) = gcd(A011772(n), A344875(n));

Formula

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

a(n) = gcd(A011772(n), A344876(n)) = gcd(A344875(n), A344876(n)) = gcd(A011772(n), A344973(n)).