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

Author

Jonathan Vos Post, Nov 24 2010

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A000001, A063756, A066085, A066083.

Programs

PARI

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

Formula

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.