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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-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)); }; 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.)