cp's OEIS Frontend

A336941 Number of strict chains of divisors starting with the superprimorial A006939(n) and ending with 1.

%I A336941 #14 Aug 30 2020 20:23:11
%S A336941 1,1,8,604,691968,16359233536,10083474928244288,
%T A336941 195661337707783118840768,139988400203593571474134024847360,
%U A336941 4231553868972506381329450624389969130848256,6090860257621637852755610879241895108657182173073604608,464479854191019594417264488167571483344961210693790188774166838214656
%N A336941 Number of strict chains of divisors starting with the superprimorial A006939(n) and ending with 1.
%H A336941 Andrew Howroyd, <a href="/A336941/b336941.txt">Table of n, a(n) for n = 0..25</a>
%F A336941 a(n) = A337070(n)/2 for n > 0.
%F A336941 a(n) = A074206(A006939(n)).
%e A336941 The a(2) = 8 chains:
%e A336941   12/1
%e A336941   12/2/1
%e A336941   12/3/1
%e A336941   12/4/1
%e A336941   12/6/1
%e A336941   12/4/2/1
%e A336941   12/6/2/1
%e A336941   12/6/3/1
%t A336941 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A336941 chns[n_]:=If[n==1,1,Sum[chns[d],{d,Most[Divisors[n]]}]];
%t A336941 Table[chns[chern[n]],{n,0,3}]
%o A336941 (PARI) a(n)={my(sig=vector(n,i,i), m=vecsum(sig)); sum(k=0, m, prod(i=1, #sig, binomial(sig[i]+k-1, k-1))*sum(r=k, m, binomial(r,k)*(-1)^(r-k)))} \\ _Andrew Howroyd_, Aug 30 2020
%Y A336941 A022915 is the maximal case.
%Y A336941 A076954 can be used instead of A006939.
%Y A336941 A336571 is the case with distinct prime multiplicities.
%Y A336941 A336942 is the case using members of A130091.
%Y A336941 A337070 is the version ending with any divisor of A006939(n).
%Y A336941 A000005 counts divisors.
%Y A336941 A074206 counts chains of divisors from n to 1.
%Y A336941 A006939 lists superprimorials or Chernoff numbers.
%Y A336941 A067824 counts divisor chains starting with n.
%Y A336941 A181818 gives products of superprimorials, with complement A336426.
%Y A336941 A253249 counts chains of divisors.
%Y A336941 A317829 counts factorizations of superprimorials.
%Y A336941 A336423 counts chains using A130091, with maximal case A336569.
%Y A336941 Cf. A000142, A001055, A002033, A008480, A022559, A027423, A124010, A167865, A181796, A336417, A336420, A337069.
%K A336941 nonn
%O A336941 0,3
%A A336941 _Gus Wiseman_, Aug 13 2020
%E A336941 Terms a(8) and beyond from _Andrew Howroyd_, Aug 30 2020