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 A128604 Number of groups of order A128603(n). 11
 1, 1, 2, 1, 1, 5, 2, 1, 1, 14, 1, 1, 1, 2, 5, 1, 1, 51, 1, 1, 1, 1, 2, 1, 1, 1, 267, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 67, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Number of groups whose order divides p^6 for p a prime. The groups of these orders (up to A128603(54403784) = 1073741789 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA. (corrected Mar 18 2007) LINKS Klaus Brockhaus, Table of n, a(n) for n = 1..10000 MAGMA Documentation, Database of Small Groups Index entries for sequences related to groups FORMULA a(n) = A000001(A128603(n)). EXAMPLE A128603(10) = 16 and there are 14 groups of order 16 (A000001(16) = 14), hence a(10) = 14. PROG (Magma) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ k: k in [1..455] | exists(t) {x: x in [t: t in [1..6] ] | IsPower(k, x) and IsPrime(Iroot(k, x)) } ] ]; CROSSREFS Cf. A000001 (number of groups of order n), A128603 (numbers dividing p^6 for p a prime), A098885 (number of groups of prime power orders). Sequence in context: A162470 A343234 A174004 * A098885 A106270 A319171 Adjacent sequences: A128601 A128602 A128603 * A128605 A128606 A128607 KEYWORD nonn AUTHOR Klaus Brockhaus, Mar 13 2007 STATUS approved

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Last modified September 27 07:56 EDT 2023. Contains 365674 sequences. (Running on oeis4.)