A184335 Numbers k such that A000001(k) > 1 and A000001(k) | k.

4, 6, 10, 14, 20, 22, 26, 28, 34, 38, 42, 44, 46, 50, 58, 62, 74, 75, 76, 78, 82, 86, 90, 92, 94, 106, 114, 118, 122, 124, 125, 134, 135, 142, 146, 158, 166, 172, 178, 186, 188, 194, 202, 204, 206, 214, 218, 222, 226, 236, 254, 258

Offset: 1

Author

Jonathan Vos Post, Feb 13 2011

Keywords

• nonn
• easy

Comments

Numbers k such that the number of groups of order k (when greater than 1) divides the group order k. I require a proper divisor > 1 because trivially for any p there is 1 group (the cyclic group) of order p, and 1 | p. Even semiprimes A100484 are a proper subset, because when k = p*q for primes p and q, then A000001(k) = 1 if gcd(p,q-1) = 1, 2 if gcd(p,q-1) = p, and (p < q).

Examples

			a(11) = 42 is in the sequence because there are 6 nonisomorphic groups of order 42, and 42/6 = 7.
a(18) = 75 is the first odd value, because there are 5 nonisomorphic groups of order 75, and 75/5 = 15. The next odd value is 125.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..324

Crossrefs

Cf. A000001, A100484.

Extensions

a(44) - a(52) from Nathaniel Johnston, Apr 26 2011