A063275 Numbers that require three powerful numbers (definition 1) to sum to them.

3, 6, 11, 14, 19, 21, 22, 30, 38, 39, 42, 46, 47, 51, 55, 56, 60, 62, 66, 67, 69, 70, 71, 75, 77, 78, 79, 83, 84, 86, 92, 93, 94, 95, 102, 103, 105, 107, 110, 114, 115, 118, 120, 123, 131, 138, 139, 142, 143, 147, 151, 154, 156, 158, 159, 163, 165, 166, 167, 168, 175

Offset: 1

Author

Jud McCranie, Jul 13 2001

Keywords

• nonn

Examples

			The powerful numbers (A001694) start 1, 4, 8, 9, ... Now 11 = 1+1+9 and is not the sum of fewer terms, so 11 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001694, A056828, A063274.

Programs

Mathematica

With[{m = 200}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; s2 = Select[Union[Plus @@@ Tuples[pow, {2}]], # <= m &]; s3 = Select[Union[Plus @@@ Tuples[pow, {3}]], # <= m &]]; Complement[s3, pow, s2] (* Amiram Eldar, Feb 12 2023 *)

Extensions

Offset corrected by Amiram Eldar, Feb 12 2023