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A101872 Number of Abelian groups of order 2n. 5
1, 2, 1, 3, 1, 2, 1, 5, 2, 2, 1, 3, 1, 2, 1, 7, 1, 4, 1, 3, 1, 2, 1, 5, 2, 2, 3, 3, 1, 2, 1, 11, 1, 2, 1, 6, 1, 2, 1, 5, 1, 2, 1, 3, 2, 2, 1, 7, 2, 4, 1, 3, 1, 6, 1, 5, 1, 2, 1, 3, 1, 2, 2, 15, 1, 2, 1, 3, 1, 2, 1, 10, 1, 2, 2, 3, 1, 2, 1, 7, 5, 2, 1, 3, 1, 2, 1, 5, 1, 4, 1, 3, 1, 2, 1, 11, 1, 4, 2, 6, 1, 2, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = A000688(2n).

Multiplicative with a(2^k) = A000041(1+k), and for odd primes p, a(p^k) = A000041(k), where A000041(k) is the number of partitions of k. - Antti Karttunen, Sep 27 2018

MATHEMATICA

Table[FiniteAbelianGroupCount[2 k], {k, 1, 100}] (* Geoffrey Critzer, Dec 29 2014 *)

PROG

(PARI) A101872(n) = factorback(apply(e -> numbpart(e), factor(2*n)[, 2])); \\ Antti Karttunen, Sep 27 2018

CROSSREFS

Bisection of A000688. Cf. also A101876 (bisection of this sequence).

Sequence in context: A330569 A340785 A206778 * A251659 A174892 A317656

Adjacent sequences:  A101869 A101870 A101871 * A101873 A101874 A101875

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane, Jan 28 2005

EXTENSIONS

More terms from Joshua Zucker, May 10 2006

STATUS

approved

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)