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A271811
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Number of non-abelian groups of order prime(n)^6.
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2
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256, 493, 673, 849, 1181, 1465, 1933, 2253, 2865, 4057, 4529, 6001, 7053, 7653, 8841, 10897, 13125, 14001, 16509, 18281, 19285, 22233, 24285, 27637, 32461, 34953, 36273, 38901, 40345, 43117, 53769, 56981, 62053, 63813, 72817, 74729, 80521, 86493, 90561, 96937, 103485, 105801, 117281
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OFFSET
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1,1
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COMMENTS
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A000688(p^6) is 11 for all prime p.
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LINKS
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FORMULA
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For a prime p > 3, the number of non-abelian groups of order p^6 is 3p^2 + 39p + 333 + 24 gcd(p - 1, 3) + 11 gcd(p - 1, 4) + 2 gcd(p - 1, 5).
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MATHEMATICA
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PROG
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(PARI) a(n) = if (n==1, 256, if (n==2, 493, my(p=prime(n)); 3*p^2 + 39*p + 333 + 24*gcd(p - 1, 3) + 11*gcd(p - 1, 4) + 2*gcd(p - 1, 5)));
(GAP) A271811 := Concatenation([256, 493], List(Filtered([5..10^4], IsPrime), p -> 3 * p^2 + 39 * p + 333 + 24 * Gcd(p-1, 3) + 11 * Gcd(p-1, 4) + 2 * Gcd(p-1, 5))); # Muniru A Asiru, Nov 18 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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