

A212642


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


6



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, 26, 22, 13, 27, 25, 19, 30, 28, 21, 14, 30, 30, 28, 34, 34, 27, 15, 33, 35, 37, 20, 38, 40, 33, 31, 16, 36, 40, 46, 15, 28, 30, 42, 46, 39, 43, 17, 39, 45, 55, 25, 35
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OFFSET

1,2


COMMENTS

Also, number of divisors of A181800 that are members of A025487.
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.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A085082(A181800(n)).


EXAMPLE

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:
{ }: 1 (multiset of positive exponents is the empty multiset)
{1}: 2 (2^1), 3 (3^1)
{1,1}: 6 (2^1*3^1)
{2}: 4 (2^2), 9 (3^2),
{2,1}: 12 (2^2*3^1), 18 (2^1*3^2)
{2,2}: 36 (2^2*3^2)
Since 36 = A181800(6), a(6) = 6.


CROSSREFS

Cf. A181800, A085082, A212171, A212172, A212643, A212644.
Sequence in context: A217031 A104136 A198466 * A159624 A320727 A036288
Adjacent sequences: A212639 A212640 A212641 * A212643 A212644 A212645


KEYWORD

nonn


AUTHOR

Matthew Vandermast, Jun 05 2012


STATUS

approved



