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.

1, 0, 1, 1, 6, 21, 110, 904, 4312, 74400, 731412, 5600761, 128196024, 792051157, 18696610816, 264267572121, 7136433698464, 57948743342529, 2228312959187256, 22463157401776612, 681974906329502904, 15395459281239915282, 463374873030990445252, 6091833036158810701465

Offset: 0

Author

Alois P. Heinz, Jul 18 2023

Keywords

• nonn

Examples

			a(0) = 1: ().
a(2) = 1: (22).
a(3) = 1: (333).
a(4) = 6: (4422), (4242), (4224), (2442), (2424), (2244).
a(5) = 21: (55555), (44333), (43433), (43343), (43334), (34433), (34343), (34334), (33443), (33434), (33344), (33322), (33232), (33223), (32332), (32323), (32233), (23332), (23323), (23233), (22333).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..444

Crossrefs

Cf. A000040, A178682, A334370, A364327, A364344.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+add(
     `if`(d>n, 0, b(n-d, i-1)*binomial(n, d)), d=numtheory[factorset](i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);