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A344973 a(n) = A344875(n) mod A011772(n). 10
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 3, 0, 0, 0, 0, 13, 0, 8, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 10, 0, 0, 16, 0, 0, 0, 16, 0, 6, 5, 20, 0, 30, 0, 0, 15, 6, 0, 24, 0, 42, 0, 0, 0, 11, 0, 28, 21, 0, 23, 5, 0, 0, 21, 12, 0, 57, 0, 0, 0, 14, 18, 0, 0, 60, 0, 0, 0, 36, 30, 40, 27, 22, 0, 26, 7, 16, 0, 44, 15, 0, 0, 0, 36 (list; graph; refs; listen; history; text; internal format)
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

FORMULA

a(n) = A344875(n) mod A011772(n) = A344876(n) mod A011772(n).

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-Fran├žois 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)); };

A344973(n) = (A344875(n)%A011772(n));

CROSSREFS

Cf. A011772, A344875, A344876, A344969, A344970, A344971, A344972.

Cf. A344974 (positions of zeros).

Sequence in context: A094830 A196878 A209835 * A298528 A341325 A021947

Adjacent sequences:  A344970 A344971 A344972 * A344974 A344975 A344976

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 04 2021

STATUS

approved

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Last modified May 22 17:42 EDT 2022. Contains 353957 sequences. (Running on oeis4.)