

A212646


a(n) = number of Abelian groups of order A181800(n) (nth powerful number that is the first integer of its prime signature).


1



1, 2, 3, 5, 7, 4, 11, 6, 15, 10, 9, 22, 14, 15, 30, 22, 21, 8, 42, 30, 25, 33, 12, 56, 44, 35, 45, 20, 77, 60, 55, 18, 66, 28, 49, 101, 84, 75, 30, 90, 44, 77, 135, 112, 110, 42, 27, 126, 60, 105, 50, 176, 154, 150, 66, 16, 121, 45, 168, 88, 154, 70, 231, 202
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OFFSET

1,2


COMMENTS

The number of Abelian groups of order n, or A000688(n), is a function of the second signature of n (cf. A212172). Since A181800 gives the first integer of each second signature, this sequence gives the value of A000688 for each second signature in order of its first appearance.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Abelian Group


FORMULA

a(n) = A000688(A181800(n)).


EXAMPLE

There are 6 Abelian groups of order 72, corresponding to the 6 factorizations of 72 into prime powers: 2^3*3^2, 2^3*3*3, 2^2*2*3^2, 2^2*2*3*3, 2*2*2*3^2, and 2*2*2*3*3. Since 72 = A181800(8), a(8) = 6.


CROSSREFS

Cf. A000688, A046054, A046055, A046056, A050360, A181800, A212172.
Sequence in context: A125151 A302024 A273665 * A103866 A268711 A191439
Adjacent sequences: A212643 A212644 A212645 * A212647 A212648 A212649


KEYWORD

nonn


AUTHOR

Matthew Vandermast, Jun 09 2012


STATUS

approved



