cp's OEIS Frontend

A337104 Number of strict chains of divisors from n! to 1 using terms of A130091 (numbers with distinct prime multiplicities).

%I A337104 #14 May 08 2021 08:30:30
%S A337104 1,1,1,0,14,0,384,0,0,0,21077680,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A337104 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A337104 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A337104 Number of strict chains of divisors from n! to 1 using terms of A130091 (numbers with distinct prime multiplicities).
%C A337104 The support appears to be {0, 1, 2, 4, 6, 10}.
%F A337104 a(n) = A337075(n) whenever A337075(n) != 0.
%F A337104 a(n) = A337074(n)/2 for n > 1.
%F A337104 a(n) = A336423(n!).
%e A337104 The a(4) = 14 chains:
%e A337104   24/1
%e A337104   24/2/1
%e A337104   24/3/1
%e A337104   24/4/1
%e A337104   24/8/1
%e A337104   24/12/1
%e A337104   24/4/2/1
%e A337104   24/8/2/1
%e A337104   24/8/4/1
%e A337104   24/12/2/1
%e A337104   24/12/3/1
%e A337104   24/12/4/1
%e A337104   24/8/4/2/1
%e A337104   24/12/4/2/1
%t A337104 strchns[n_]:=If[n==1,1,If[!UnsameQ@@Last/@FactorInteger[n],0,Sum[strchns[d],{d,Select[DeleteCases[Divisors[n],n],UnsameQ@@Last/@FactorInteger[#]&]}]]];
%t A337104 Table[strchns[n!],{n,0,8}]
%Y A337104 A336867 appears to be the positions of zeros.
%Y A337104 A336868 is the characteristic function (image under A057427).
%Y A337104 A336942 is the version for superprimorials (n > 1).
%Y A337104 A337105 does not require distinct prime multiplicities.
%Y A337104 A337074 does not require chains to end with 1.
%Y A337104 A337075 is the version for chains not containing n!.
%Y A337104 A000005 counts divisors.
%Y A337104 A000142 lists factorial numbers.
%Y A337104 A001055 counts factorizations.
%Y A337104 A027423 counts divisors of factorial numbers.
%Y A337104 A067824 counts chains of divisors starting with n.
%Y A337104 A074206 counts chains of divisors from n to 1.
%Y A337104 A130091 lists numbers with distinct prime multiplicities.
%Y A337104 A181796 counts divisors with distinct prime multiplicities.
%Y A337104 A253249 counts chains of divisors.
%Y A337104 A327498 gives the maximum divisor with distinct prime multiplicities.
%Y A337104 A336414 counts divisors of n! with distinct prime multiplicities.
%Y A337104 A336423 counts chains using A130091, with maximal case A336569.
%Y A337104 A336425 counts divisible pairs of divisors of n!, both in A130091.
%Y A337104 A336571 counts chains of divisors 1 < d < n using A130091.
%Y A337104 A337071 counts chains of divisors starting with n!.
%Y A337104 Cf. A002033, A022559, A071626, A098859, A124010, A167865, A327523, A336424, A336941.
%K A337104 nonn
%O A337104 0,5
%A A337104 _Gus Wiseman_, Aug 17 2020