A113883 -id:A113883 - cp's OEIS frontend

A325630 Numbers k such that A000110(k) is divisible by k.

1, 2, 35, 16833, 16989, 23684

Offset: 1

Vaclav Kotesovec, Sep 07 2019

No other terms below 50000.
From Amiram Eldar, Jun 20 2024: (Start)
Numbers k such that A166226(k) = 0.
All the terms above 2 are composites since A166226(p) == 2 (mod p) for prime p. (End)
No other terms below 90000. - Michael S. Branicky, Jan 09 2025

			35 is in the sequence because A000110(35) = 35 * 8045720086273150473238297902.

Cf. A000110, A051130, A066562, A073877, A113883, A166226, A280727, A325935.

Cf. A014847, A016089, A023172, A051177, A056848.

Select[Range[1000], Divisible[BellB[#], #] &]

A113908 Number of prime factors, with multiplicity, of Bell number A000110(n).

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 2, 1, 6, 4, 3, 4, 3, 1, 3, 3, 2, 7, 3, 4, 6, 4, 6, 4, 3, 6, 5, 6, 4, 6, 6, 2, 5, 2, 4, 7, 4, 3, 4, 3, 3, 6, 1, 7, 6, 5, 4, 8, 4, 2, 5, 3, 5, 6, 3, 1, 12, 3, 3, 5, 3, 7, 3, 7, 4, 5, 6, 3, 5, 4, 4, 10, 9, 6, 6, 5, 8, 5, 5, 8, 5, 4, 5, 3, 2

Offset: 0

Jonathan Vos Post, Jan 29 2006

nonn

This is 1 for A051330 (indices of prime Bell numbers) and is 2 for A113883 (indices of semiprime Bell numbers). The records begin a(0) = 0, a(2) = 1, a(4) = 2, a(5) = 3, a(8) = 6, a(17) = 7, a(56) = 12.

			a(5) = BigOmega(Bell(5)) = A001222(52) = A001222(2^2 * 13) = 3.

Amiram Eldar, Table of n, a(n) for n = 0..104
John Sokol, The First 1000 Bell Numbers.

Cf. A000110, A001222, A113015, A113883.

with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(bell(n)) fi end: seq(a(n), n=0..43); # Zerinvary Lajos, Apr 11 2008

Table[PrimeOmega[BellB[n]], {n, 0, 50}] (* Amiram Eldar, Nov 23 2019 *)

a(n) = BigOmega(A000110(n)). a(n) = A001222(A000110(n)).

cp's OEIS Frontend

A325630 Numbers k such that A000110(k) is divisible by k.

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