cp's OEIS Frontend

A336425 Number of ways to choose a divisor with distinct prime exponents of a divisor with distinct prime exponents of n!.

%I A336425 #14 Nov 10 2024 05:09:19
%S A336425 1,1,3,5,24,38,132,195,570,1588,4193,6086,14561,19232,37142,106479,
%T A336425 207291,266871,549726,674330,1465399,3086598,5939574,7182133,12324512,
%U A336425 28968994,46819193,82873443,165205159,196666406,350397910,406894074,593725529,1229814478,1853300600,4024414209,6049714096,6968090487,9700557121,16810076542,26339337285
%N A336425 Number of ways to choose a divisor with distinct prime exponents of a divisor with distinct prime exponents of n!.
%H A336425 Max Alekseyev, <a href="/A336425/b336425.txt">Table of n, a(n) for n = 0..85</a>
%e A336425 The a(4) = 24 divisors of divisors:
%e A336425   1/1  2/1  3/1  4/1  8/1  12/1   24/1
%e A336425        2/2  3/3  4/2  8/2  12/2   24/2
%e A336425                  4/4  8/4  12/3   24/3
%e A336425                       8/8  12/4   24/4
%e A336425                            12/12  24/8
%e A336425                                   24/12
%e A336425                                   24/24
%t A336425 strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n];
%t A336425 Table[Total[Cases[Divisors[n!],d_?strsigQ:>Count[Divisors[d],e_?strsigQ]]],{n,0,20}]
%Y A336425 A336422 is the non-factorial generalization.
%Y A336425 A130091 lists numbers with distinct prime exponents.
%Y A336425 A181796 counts divisors with distinct prime exponents.
%Y A336425 A327526 gives the maximum divisor of n with equal prime exponents.
%Y A336425 A327498 gives the maximum divisor of n with distinct prime exponents.
%Y A336425 A336414 counts divisors of n! with distinct prime exponents.
%Y A336425 A336415 counts divisors of n! with equal prime exponents.
%Y A336425 A336423 counts chains in A130091, with maximal version A336569.
%Y A336425 Cf. A000005, A000110, A098859, A118914, A124010, A336424, A336500, A336568, A336570, A336571, A336865, A336866, A336869.
%Y A336425 Factorial numbers: A000142, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A327499, A336416, A336418, A336617.
%K A336425 nonn
%O A336425 0,3
%A A336425 _Gus Wiseman_, Aug 06 2020
%E A336425 Terms a(21) onward from _Max Alekseyev_, Nov 07 2024