A097214 Numbers m such that A076078(m) = m, where A076078(m) equals the number of sets of distinct positive integers with a least common multiple of m.

1, 2, 4, 8, 10, 16, 32, 44, 64, 128, 184, 256, 512, 752, 1024, 2048, 4096, 8192, 12224, 16384, 32768, 49024, 61064, 65536, 131072, 262144, 524288, 981520, 1048576, 2097152, 4194304, 8388608, 12580864, 16777216, 33554432, 67108864, 134217728

Offset: 1

Author

Matthew Vandermast, Aug 12 2004

Keywords

• nonn

Comments

Contains all powers of 2 (A000079). Union of A000079 and A097215.

If 3*2^k - 1 is prime then 2^k*(3*2^k-1) is in the sequence. So 2^A002235*(3*2^A002235-1) is a subsequence of this sequence. - Farideh Firoozbakht, Aug 06 2005

Examples

			A total of 10 sets of distinct positive integers have a least common multiple of 10: {1,2,5}, {1,2,5,10}, {1,2,10}, {1,5,10}, {1,10}, {2,5}, {2,5,10}, {2,10}, {5,10} and {10}. Hence 10 is in the sequence.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..334

Crossrefs

Cf. A076078, A097215.

Cf. A002235.

Extensions

a(26) corrected by Jinyuan Wang, Feb 11 2020