cp's OEIS Frontend

A364328 Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a prime divisor of i.

%I A364328 #15 Jul 20 2023 10:39:05
%S A364328 1,0,1,1,6,21,110,904,4312,74400,731412,5600761,128196024,792051157,
%T A364328 18696610816,264267572121,7136433698464,57948743342529,
%U A364328 2228312959187256,22463157401776612,681974906329502904,15395459281239915282,463374873030990445252,6091833036158810701465
%N A364328 Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a prime divisor of i.
%H A364328 Alois P. Heinz, <a href="/A364328/b364328.txt">Table of n, a(n) for n = 0..444</a>
%e A364328 a(0) = 1: ().
%e A364328 a(2) = 1: (22).
%e A364328 a(3) = 1: (333).
%e A364328 a(4) = 6: (4422), (4242), (4224), (2442), (2424), (2244).
%e A364328 a(5) = 21: (55555), (44333), (43433), (43343), (43334), (34433), (34343), (34334), (33443), (33434), (33344), (33322), (33232), (33223), (32332), (32323), (32233), (23332), (23323), (23233), (22333).
%p A364328 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+add(
%p A364328      `if`(d>n, 0, b(n-d, i-1)*binomial(n, d)), d=numtheory[factorset](i))))
%p A364328     end:
%p A364328 a:= n-> b(n$2):
%p A364328 seq(a(n), n=0..23);
%Y A364328 Cf. A000040, A178682, A334370, A364327, A364344.
%K A364328 nonn
%O A364328 0,5
%A A364328 _Alois P. Heinz_, Jul 18 2023