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%I #16 Jan 21 2024 02:23:33
%S 1,2,3,3,4,5,5,7,4,6,6,9,7,7,9,11,10,8,12,9,13,5,10,13,9,15,14,15,9,
%T 14,16,10,18,19,17,13,18,10,19,11,16,21,12,15,24,19,17,22,16,22,12,23,
%U 24,6,19,20,29,21,21,26,22,25,13,30,27,11,26,25,19,34
%N Number of distinct prime signatures that occur among the divisors of the n-th prime signature number (A025487(n)).
%C Also the number of members of A025487 that divide A025487(n).
%H Amiram Eldar, <a href="/A238746/b238746.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A085082(A025487(n)) = A085082(A181822(n)).
%F a(n) = A322584(A025487(n)). - _Amiram Eldar_, Jan 21 2024
%e 5 members of A025487 divide A025487(6) = 12 (namely, 1, 2, 4, 6 and 12); therefore, a(6) = 5.
%t lpsQ[n_] := n == 1 || (Max@ Differences[(f = FactorInteger[n])[[;;,2]]] < 1 && f[[-1, 1]] == Prime[Length[f]]); lps = Select[Range[6000], lpsQ]; c[n_] := Count[Divisors[n], _?(MemberQ[lps, #] &)]; c /@ lps (* _Amiram Eldar_, Jan 21 2024 *)
%Y Cf. A085082, A025487, A181822, A322584.
%Y Rearrangement of A115728, A115729 and A238690.
%Y A116473(n) is the number of times n appears in the sequence.
%K nonn
%O 1,2
%A _Matthew Vandermast_, Apr 28 2014
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