cp's OEIS Frontend

A336870 Irregular triangle read by rows where T(n,k) is the number of divisors d of the superprimorial A006939(n) with k prime factors (counting multiplicity), such that d and A006939(n)/d both have distinct prime multiplicities.

%I A336870 #11 Aug 10 2020 00:24:13
%S A336870 1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,4,4,2,4,4,1,1,1,1,1,1,4,4,7,7,7,7,
%T A336870 7,7,4,4,1,1,1,1,1,1,4,4,7,18,10,10,15,21,21,15,10,10,18,7,4,4,1,1,1,
%U A336870 1,1,1,4,4,7,18,23,15,20,37,35,40,46,32,46,40,35,37,20,15,23,18,7,4,4,1,1,1
%N A336870 Irregular triangle read by rows where T(n,k) is the number of divisors d of the superprimorial A006939(n) with k prime factors (counting multiplicity), such that d and A006939(n)/d both have distinct prime multiplicities.
%C A336870 Are there any zeros (cf. A336939)?
%C A336870 A number has distinct prime multiplicities iff its prime signature is strict.
%e A336870 Triangle begins:
%e A336870   1
%e A336870   1 1
%e A336870   1 1 1 1
%e A336870   1 1 1 4 1 1 1
%e A336870   1 1 1 4 4 2 4 4 1 1 1
%e A336870   1 1 1 4 4 7 7 7 7 7 7 4 4 1 1 1
%e A336870 Row n = 4 counts the following divisors:
%e A336870   1  7  25   27   16  112   400   432  3024  10800  75600
%e A336870              63   54  675  1350  1008
%e A336870              75   56       1400  1200
%e A336870             175  189       4725  2800
%t A336870 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A336870 Table[Length[Select[Divisors[chern[n]],UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[chern[n]/#]&&PrimeOmega[#]==k&]],{n,0,6},{k,0,PrimeOmega[chern[n]]}]
%Y A336870 A000124 gives row lengths.
%Y A336870 A336419 gives row sums.
%Y A336870 A336500 is the generalization to all positive integers.
%Y A336870 A336939 is the version for factorials.
%Y A336870 A000005 counts divisors.
%Y A336870 A000110 counts divisors of superprimorials with distinct prime multiplicities.
%Y A336870 A000142 lists factorials.
%Y A336870 A000325 counts divisors of superprimorials with equal prime multiplicities.
%Y A336870 A006939 lists superprimorials.
%Y A336870 A130091 lists numbers with distinct prime multiplicities.
%Y A336870 A181796 counts divisors with distinct prime multiplicities.
%Y A336870 A327498 gives the maximum divisor of n with distinct prime multiplicities.
%Y A336870 A336423 counts chains using A130091.
%Y A336870 Cf. A022559, A027423, A048742, A071626, A098859, A118914, A124010, A336414, A336424, A336568, A336571, A336865, A336869.
%K A336870 nonn,tabf
%O A336870 0,11
%A A336870 _Gus Wiseman_, Aug 08 2020