# [seqfan] Re: Divisibilty sequences

Valery Liskovets liskov at im.bas-net.by
Mon Mar 30 10:46:52 CEST 2009

```I touched briefly related questions in the last section of my article
"Some easily derivable sequences", J. Integer Sequences, 3 (2000), #00.2.2
(http://www.cs.uwaterloo.ca/journals/JIS/index.html ).

Here are two simple examples from (planar) map enumeration:
A003645(n)=2^n*Cat(n+1)=A000079(n)*A000108(n+1)
A005159(n)=3^n*Cat(n), that is, A005159=A000244*A000108.

Valery Liskovets

Richard Guy wrote:

> Towards a multiplicative theory of divisibility sequences.
>
> A001542 = 2 * (A001109)
> A003690 = 3 * (A004254)^2
> A003696 = (A001353) * (b=14,c=68)  latter not in OEIS?
> A003733 = 5 * (A143699)^2
> A003739 = 5 * (A001906) * (A006238)
> A003745 = 3 * 5^2 * (A004254) * (A004187)^3
> A003751 = 5^3 * (A004187)^4
> A003753 = 2^2 * (A001109) * (A001353)^2
>          = 2 * (A001542) * (A001353)^2
> A003755 = (A001109) * (A001906)^2
> A003761 = (A001906) * (A004254) * (A001109)
> A003767 = 2^3 * (A001353) * (A001109)^2
> A003773 = 2 * (A001542)^3 = 2^4 * (A001109)^3
> A092136 = (A004187) * (A001906)^3
>
> E&OE     R,
>
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```