A392872 a(n) = A122111(n) mod prime(1+bigomega(n)).

1, 2, 1, 3, 2, 1, 1, 5, 4, 2, 2, 3, 1, 4, 3, 7, 2, 1, 1, 6, 1, 3, 2, 3, 2, 1, 4, 5, 1, 2, 2, 11, 2, 2, 4, 10, 1, 4, 4, 6, 2, 4, 1, 3, 1, 3, 2, 9, 1, 3, 3, 6, 1, 2, 3, 1, 1, 1, 2, 9, 1, 2, 2, 13, 1, 1, 2, 5, 2, 6, 1, 7, 2, 4, 5, 3, 2, 2, 1, 5, 5, 3, 2, 7, 2, 1, 4, 2, 1, 4, 4, 6, 3, 2, 4, 9, 2, 2, 4, 8, 1, 4, 2, 4, 3

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to prime indices in the factorization of n.

Formula

a(n) = A392865(A122111(n)) = A122111(n) mod A000040(1+A001222(n)).

a(2^n) = A000040(n).

Mathematica

a122111[n_] := Function[l, Product[Prime[Sum[If[j<i, 0, 1], {j, l}]], {i, 1, Max[l]}]][Flatten[Table[Table[PrimePi[f[[1]]], {f[[2]]}], {f, FactorInteger[n]}]]]; a[n_]:=Mod[a122111[n], Prime[1+PrimeOmega[n]]]; Array[a, 105] (* James C. McMahon, Jan 27 2026 *)

Prog

(PARI)
A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A392872(n) = (A122111(n)%prime(1+bigomega(n)));

Crossrefs

Cf. A000040, A001222, A105560, A122111, A392865.

Cf. also A392866, A392874, A392875, A392876 for other similar sequences.

Sequence in context: A375378 A295665 A103484 * A016444 A280831 A166948

Adjacent sequences: A392869 A392870 A392871 * A392873 A392874 A392875

Keyword

nonn,easy

Author

Antti Karttunen, Jan 27 2026

Status

approved