cp's OEIS Frontend

A337075 Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities) starting with a proper divisor of n! and ending with 1.

%I A337075 #11 Nov 20 2020 17:16:07
%S A337075 1,1,1,3,14,48,384,1308,40288,933848,21077680,75690016,5471262080,
%T A337075 7964665440,54595767744,17948164982144,3454946386353664,
%U A337075 5010658671663616,723456523262697984,950502767770273280,165679731871366906880,8443707247468681128448
%N A337075 Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities) starting with a proper divisor of n! and ending with 1.
%F A337075 a(n) = A337104(n) whenever A337104(n) != 0.
%F A337075 a(n) = A336571(n!).
%e A337075 The a(1) = 1 through a(4) = 14 chains (with n! prepended):
%e A337075   1  2/1  6/1    24/1
%e A337075           6/2/1  24/2/1
%e A337075           6/3/1  24/3/1
%e A337075                  24/4/1
%e A337075                  24/8/1
%e A337075                  24/12/1
%e A337075                  24/4/2/1
%e A337075                  24/8/2/1
%e A337075                  24/8/4/1
%e A337075                  24/12/2/1
%e A337075                  24/12/3/1
%e A337075                  24/12/4/1
%e A337075                  24/8/4/2/1
%e A337075                  24/12/4/2/1
%t A337075 chnstr[n_]:=If[n==1,1,Sum[chnstr[d],{d,Select[Most[Divisors[n]],UnsameQ@@Last/@FactorInteger[#]&]}]];
%t A337075 Table[chnstr[n!],{n,0,5}]
%Y A337075 A336571 is the generalization to not just factorial numbers.
%Y A337075 A337104 is the version for chains containing n!.
%Y A337075 A000005 counts divisors.
%Y A337075 A001055 counts factorizations.
%Y A337075 A032741 counts proper divisors.
%Y A337075 A071625 counts distinct prime multiplicities.
%Y A337075 A074206 counts chains of divisors from n to 1.
%Y A337075 A130091 lists numbers with distinct prime multiplicities.
%Y A337075 A181796 counts divisors with distinct prime multiplicities.
%Y A337075 A253249 counts chains of divisors.
%Y A337075 A327498 gives the maximum divisor with distinct prime multiplicities.
%Y A337075 A336414 counts divisors of n! with distinct prime multiplicities.
%Y A337075 A336423 counts chains using A130091, with maximal case A336569.
%Y A337075 A336424 counts factorizations using A130091.
%Y A337075 A336425 counts divisible pairs of divisors of n!, both in A130091.
%Y A337075 Cf. A002033, A098859, A124010, A294068, A327499, A327500, A327523, A337071.
%K A337075 nonn
%O A337075 0,4
%A A337075 _Gus Wiseman_, Aug 17 2020