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Search: id:A090140
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| A090140 |
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Number of groups of order 7^n. |
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+0
3
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OFFSET
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0,3
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REFERENCES
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G. Bagnera, La composizione dei Gruppi finiti il cui grado e la quinta potenza di un numero primo, Ann. Mat. Pura Appl. (3), 1 (1898), 137-228.
Hans Ulrich Besche, Bettina Eick and E. A. O'Brien, A Millenium Project: Constructing Small Groups, International Journal of Algebra and Computation, Vol. 12, No 5 (2002), 623-644.
W. Burnside, Theory of Groups of Finite Order, Dover, NY, 1955.
M. F. Newman, E. A. O'Brien and M. R. Vaughan-Lee, Groups and nilpotent Lie rings whose order is the sixth power of a prime, J. Algebra, 278 (2004), 383-401.
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FORMULA
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For a prime p >= 5, the number of groups of order p^n begins 1, 1, 2, 5, 15, 61 + 2*p + 2*gcd (p - 1, 3) + gcd (p - 1, 4), 3*p^2 + 39*p + 344 + 24*gcd(p - 1, 3) + 11*gcd(p - 1, 4) + 2*gcd(p - 1, 5), ...
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CROSSREFS
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Cf. A000001, A000679, A090091, A090130.
Sequence in context: A090091 A090130 A133645 this_sequence A032267 A075441 A111790
Adjacent sequences: A090137 A090138 A090139 this_sequence A090141 A090142 A090143
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KEYWORD
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nonn
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AUTHOR
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Eamonn O'Brien (obrien(AT)math.auckland.ac.nz), Jan 22 2004
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