A085955 Composites such that the number of 1's in their binary expansion is equal to the number of 1's in the binary expansion of the sum of their prime factors (counting repetition).

4, 6, 9, 16, 20, 22, 24, 28, 36, 38, 49, 56, 65, 69, 70, 72, 84, 86, 92, 100, 104, 105, 118, 130, 132, 133, 134, 138, 148, 150, 152, 153, 162, 166, 176, 180, 184, 208, 209, 212, 214, 216, 256, 258, 259, 261, 262, 264, 266, 267, 278, 284, 320, 325, 326, 329, 345

Offset: 1

Author

Jason Earls, Aug 17 2003

Keywords

• easy
• nonn
• base

Examples

			a(42) = 216 because 216 = '11011000' and sopfr(216) = 15 = '1111'; both have four 1's.
		

Links

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

Crossrefs

Cf. A000120, A001414, A002808, A064548.

Programs

Mathematica

binWt[n_] := DigitCount[n, 2, 1]; seqQ[n_] := CompositeQ[n] && binWt[n] == binWt[Plus @@ Times @@@ FactorInteger[n]]; Select[Range[350], seqQ] (* Amiram Eldar, Dec 14 2019 *)