A066083 -id:A066083 - cp's OEIS frontend

A173666 Partial sums of number of supersolvable groups of order n (A066083).

1, 2, 3, 5, 6, 8, 9, 14, 16, 18, 19, 23, 24, 26, 27, 41, 42, 47, 48, 53, 55, 57, 58, 70, 72, 74, 79, 83, 84, 88, 89, 140, 141, 143, 144, 155, 156, 158, 160, 174, 175, 181, 182, 186, 188, 190, 191, 233, 235, 240, 241, 246, 247, 262, 264, 276, 278, 280, 281, 292, 293, 295, 299, 566, 567, 571, 572, 577, 578, 582, 583, 620, 621, 623, 625, 629, 630, 636, 637, 688

Offset: 1

Jonathan Vos Post, Nov 24 2010

nonn

Number of supersolvable groups of order <= n. Diverges from A063756 after n=11. The subsequence of primes in this sequence begins: 2, 3, 5, 19, 23, 41, 47, 53, 79, 83, 89, 181, 191, 233, 241, 281, 293, 571, 577. The subsequence of perfect powers in this sequence begins: 1, 8, 9, 16, 27, 144, 625.

Cf. A000001, A063756, A066085, A066083.

s=0; apply(x->s+=x,A066083) /* A066083 being defined as a vector */ \\ M. F. Hasler, Nov 25 2010

a(n) = Sum_{i=1..n} A066083 = Sum_{i=1..n} number of finite groups of order i for which the index of any maximal subgroup is prime.

A066085 Orders of non-supersolvable groups.

Original entry on oeis.org

12, 24, 36, 48, 56, 60, 72, 75, 80, 84, 96, 108, 112, 120, 132, 144, 150, 156, 160, 168, 180, 192, 196, 200, 204, 216, 224, 225, 228, 240, 252, 264, 276, 280, 288, 294, 300, 312, 320, 324, 336, 348, 351, 360, 363, 372, 375, 384, 392, 396, 400, 405, 408, 420

Offset: 1

Reiner Martin, Dec 29 2001

nonn

A finite group is supersolvable if it has a normal series with cyclic factors. Huppert showed that a finite group is supersolvable iff the index of any maximal subgroup is prime.

All multiples of non-supersolvable orders are non-supersolvable orders. - Des MacHale, Dec 22 2003

			a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.

B. Huppert, Über das Produkt von paarweise vertauschbaren zyklischen Gruppen, Math. Z. 58 (1954).
Des MacHale and J. Manning, Converse Lagrange Theorem Orders and Supersolvable Orders, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.

Cf. A000001, A066083, A340511.

For primitive terms see A340517.

More terms from Des MacHale, Dec 22 2003

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A173666 Partial sums of number of supersolvable groups of order n (A066083).

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A066085 Orders of non-supersolvable groups.

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