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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 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 * (1-A048651) * A021002 = 3.26425865613408900779... . - Amiram Eldar, Sep 23 2023 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). Cf. A000041, A021002, A048651. Sequence in context: A340785 A355758 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 December 6 01:58 EST 2023. Contains 367594 sequences. (Running on oeis4.)