A128704 Number of groups of order A128703(n).
2, 1, 1, 5, 2, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 15, 1, 4, 1, 2, 2, 1, 2, 1, 7, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 1, 1, 5, 1, 2, 2, 2, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 2, 1, 2, 55, 2, 1, 1, 2, 1, 2, 15, 1, 2, 1, 1, 2, 4, 1, 2, 1, 1, 5, 2, 2, 1, 1, 1, 1, 4, 1, 2, 1, 1, 21, 1, 1, 1, 2
Offset: 1
Keywords
Examples
A128703(20) = 275 and there are 4 groups of order 275 (A000001(275) = 4), hence a(20) = 4.
Links
- Klaus Brockhaus, Table of n, a(n) for n=1..10000
- Magma Computational Algebra System, Documentation, see Database of Small Groups.
Crossrefs
Cf. A000001 (number of groups of order n), A128703 (numbers of form 5^k*p, 1<=k<=5, p!=5 prime), A128604 (number of groups for orders that divide p^6, p prime), A128644 (number of groups for orders that have at most 3 prime factors), A128645 (number of groups for orders of form 2^k*p, 1<=k<=8, p>2 prime), A128694 (number of groups for orders of form 3^k*p, 1<=k<=6, p!=3 prime).
Programs
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Magma
D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n): n in [ h: h in [1..2000] | #t eq 2 and ((t[1, 1] lt 5 and t[1, 2] eq 1 and t[2, 1] eq 5 and t[2, 2] le 5) or (t[1, 1] eq 5 and t[1, 2] le 5 and t[2, 2] eq 1)) where t is Factorization(h) ] ];
Comments