cp's OEIS Frontend

A347957 Dirichlet convolution of A001221 (omega) with A003602 (Kimberling's paraphrases).

%I A347957 #21 Nov 18 2021 09:02:32
%S A347957 0,1,1,2,1,5,1,3,3,6,1,9,1,7,7,4,1,14,1,11,8,9,1,13,4,10,8,13,1,28,1,
%T A347957 5,10,12,9,25,1,13,11,16,1,34,1,17,22,15,1,17,5,25,13,19,1,38,11,19,
%U A347957 14,18,1,49,1,19,26,6,12,46,1,23,16,44,1,36,1,22,31,25,12,52,1,21,22,24,1,60,14,25,19,25,1,86
%N A347957 Dirichlet convolution of A001221 (omega) with A003602 (Kimberling's paraphrases).
%H A347957 Antti Karttunen, <a href="/A347957/b347957.txt">Table of n, a(n) for n = 1..16384</a>
%H A347957 Jon Maiga, <a href="http://sequencedb.net/s/A347957">Computer-generated formulas for A347957</a>, Sequence Machine.
%F A347957 a(n) = Sum_{d|n} A001221(n/d) * A003602(d).
%F A347957 From _Antti Karttunen_, Nov 13 2021: (Start)
%F A347957 The following two convolutions were found by Jon Maiga's Sequence Machine search algorithm. The first one is obvious, and even the second one should not be too hard to prove:
%F A347957 a(n) = Sum_{d|n} A023900(n/d) * A347956(d).
%F A347957 a(n) = Sum_{d|n} A181988(n/d) * A205745(d).
%F A347957 (End)
%o A347957 (PARI)
%o A347957 A003602(n) = (1+(n>>valuation(n,2)))/2;
%o A347957 A347957(n) = sumdiv(n,d,omega(n/d)*A003602(d));
%Y A347957 Cf. A001221, A003602, A023900, A181988, A205745.
%Y A347957 Cf. also A328203, A347954, A347955, A347956.
%K A347957 nonn
%O A347957 1,4
%A A347957 _Antti Karttunen_, Sep 20 2021