A344976 a(n) = A344878(n) - A011772(n).

0, 0, 0, 0, 0, 3, 0, 0, 0, 8, 0, 6, 0, -1, -1, 0, 0, 16, 0, 13, 0, 19, 0, 15, 0, 0, 0, 35, 0, -3, 0, 0, -1, 32, -2, 48, 0, -1, 0, 45, 0, -14, 0, 38, -1, 43, 0, 30, 0, 0, -1, 45, 0, 51, 10, -18, 0, 56, 0, 13, 0, -1, -3, 0, -13, 19, 0, 96, -1, -8, 0, 57, 0, 0, 0, 70, 9, 0, 0, 60, 0, 80, 0, -6, -18, -1, -1, -2, 0, -11, -1, 131

Offset

1,6

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) = A344878(n) - A011772(n).

a(n) <= A344876(n).

Mathematica

A011772[n_] := Module[{m = 1}, While[Not[IntegerQ[m(m+1)/(2n)]], m++]; m];
A344878[n_] := If[n == 1, 1, Module[{p, e}, LCM @@ Table[{p, e} = pe; (p^(e + If[p == 2, 1, 0])) - 1, {pe, FactorInteger[n]}]]];
a[n_] := A344878[n] - A011772[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
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))));
A344976(n) = (A344878(n)-A011772(n));

Crossrefs

Cf. A011772, A344876, A344878, A344977 (positions of negative terms), A344978, A344979 (positions of zeros), A344885 (and their characteristic function).

Sequence in context: A115869 A115859 A241663 * A344876 A129170 A342590

Adjacent sequences: A344973 A344974 A344975 * A344977 A344978 A344979

Keyword

sign

Author

Antti Karttunen, Jun 04 2021

Status

approved