A344970 a(n) = A011772(n) / gcd(A011772(n), A344875(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 7, 5, 1, 1, 1, 1, 15, 1, 11, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 11, 1, 7, 1, 1, 19, 1, 1, 1, 5, 1, 16, 9, 23, 1, 16, 1, 1, 17, 13, 1, 9, 1, 8, 1, 1, 1, 15, 1, 31, 9, 1, 25, 11, 1, 1, 23, 5, 1, 21, 1, 1, 1, 4, 7, 1, 1, 16, 1, 1, 1, 4, 17, 43, 29, 16, 1, 35, 13, 23, 1, 47, 19, 1, 1, 1, 11

Offset

1,12

Comments

Denominator 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

Formula

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

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_] := A011772[n]/GCD[A011772[n], A344875[n]];
Array[a, 100] (* Jean-François Alcover, Jun 12 2021 *)

Prog

(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)); };
A344970(n) = { my(u=A011772(n)); (u/gcd(u, A344875(n))); };

Crossrefs

Cf. A011772, A344875, A344969, A344971 (numerators), A344972 (ratio floored down), A344974 (positions of ones), A344980 (of terms > 1).

Sequence in context: A363974 A342633 A094649 * A135857 A156558 A082455

Adjacent sequences: A344967 A344968 A344969 * A344971 A344972 A344973

Keyword

nonn,frac

Author

Antti Karttunen, Jun 04 2021

Status

approved