A392872 - OEIS

%I #10 Jan 27 2026 22:15:30

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A392872/b392872.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

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

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

%t 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 *)

%o (PARI)

%o 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));

%o A392872(n) = (A122111(n)%prime(1+bigomega(n)));

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

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

%K nonn,easy

%O 1,2

%A _Antti Karttunen_, Jan 27 2026