OFFSET
1,12
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..11264
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
MATHEMATICA
b[n_] := If[n == 1, 1, Module[{p, e}, Product[{p, e} = pe;
If[p == 2, 2^(1 + e) - 1, p^e - 1], {pe, FactorInteger[n]}]]];
c[n_] := Module[{m = 1}, While[Not[IntegerQ[m (m + 1)/(2 n)]], m++]; m];
a[n_] := Mod[b[n], c[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)); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 04 2021
STATUS
approved