cp's OEIS Frontend

A355749 Number of ways to choose a weakly decreasing sequence of divisors, one of each prime index of n (with multiplicity, taken in weakly increasing order).

%I A355749 #5 Jul 19 2022 08:03:43
%S A355749 1,1,2,1,2,1,3,1,3,1,2,1,4,1,2,1,2,1,4,1,3,1,3,1,3,1,4,1,4,1,2,1,2,1,
%T A355749 3,1,6,1,3,1,2,1,4,1,3,1,4,1,6,1,2,1,5,1,2,1,3,1,2,1,6,1,4,1,4,1,2,1,
%U A355749 2,1,6,1,4,1,2,1,3,1,4,1,5,1,2,1,2,1,3
%N A355749 Number of ways to choose a weakly decreasing sequence of divisors, one of each prime index of n (with multiplicity, taken in weakly increasing order).
%C A355749 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%H A355749 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cartesian_product">Cartesian product</a>.
%e A355749 The a(2) = 1 through a(19) = 4 choices:
%e A355749   1  1  11  1  11  1  111  11  11  1  111  1  11  11  1111  1  111  1
%e A355749      2      3      2       21      5       2      21        7       2
%e A355749                    4       22              3                        4
%e A355749                                            6                        8
%t A355749 Table[Length[Select[Tuples[Divisors/@primeMS[n]], GreaterEqual@@#&]],{n,100}]
%Y A355749 Allowing any choice of divisors gives A355731, firsts A355732.
%Y A355749 Choosing a multiset instead of sequence gives A355733, firsts A355734.
%Y A355749 The reverse version is A355735, firsts A355736, only primes A355745.
%Y A355749 A000005 counts divisors.
%Y A355749 A001414 adds up distinct prime divisors, counted by A001221.
%Y A355749 A003963 multiplies together the prime indices of n.
%Y A355749 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A355749 A061395 selects the maximum prime index.
%Y A355749 Cf. A000720, A076610, A120383, A316524, A324850, A355737, A355739, A355740, A355741, A355742, A355744.
%K A355749 nonn
%O A355749 1,3
%A A355749 _Gus Wiseman_, Jul 18 2022