cp's OEIS Frontend

A212642 a(n) = number of distinct prime signatures represented among divisors of A181800(n) (n-th powerful number that is the first integer of its prime signature).

%I A212642 #11 Jul 14 2019 10:58:10
%S A212642 1,3,4,5,6,6,7,9,8,12,10,9,15,14,10,18,18,10,11,21,15,22,16,12,24,20,
%T A212642 26,22,13,27,25,19,30,28,21,14,30,30,28,34,34,27,15,33,35,37,20,38,40,
%U A212642 33,31,16,36,40,46,15,28,30,42,46,39,43,17,39,45,55,25,35
%N A212642 a(n) = number of distinct prime signatures represented among divisors of A181800(n) (n-th powerful number that is the first integer of its prime signature).
%C A212642 Also, number of divisors of A181800 that are members of A025487.
%C A212642 Consider a member of A181800 with second signature {S} whose divisors represent a total of k distinct second signatures and a total of (j+k) distinct prime signatures.  Let n be any integer with second signature {S}.  Then A212180(n) = k and A085082(n) is congruent to j modulo k. Cf. A212643, A212644.
%H A212642 Amiram Eldar, <a href="/A212642/b212642.txt">Table of n, a(n) for n = 1..10000</a>
%F A212642 a(n) = A085082(A181800(n)).
%e A212642 The divisors of 36 represent a total of 6 distinct prime signatures (cf. A085082), as can be seen from the positive exponents, if any, in the canonical prime factorization of each divisor:
%e A212642 { }: 1 (multiset of positive exponents is the empty multiset)
%e A212642 {1}: 2 (2^1), 3 (3^1)
%e A212642 {1,1}: 6 (2^1*3^1)
%e A212642 {2}: 4 (2^2), 9 (3^2),
%e A212642 {2,1}: 12 (2^2*3^1), 18 (2^1*3^2)
%e A212642 {2,2}: 36 (2^2*3^2)
%e A212642 Since 36 = A181800(6), a(6) = 6.
%Y A212642 Cf. A181800, A085082, A212171, A212172, A212643, A212644.
%K A212642 nonn
%O A212642 1,2
%A A212642 _Matthew Vandermast_, Jun 05 2012