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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). 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)