A115156 -id:A115156 - cp's OEIS frontend

A071814 Numbers k such that the number of 1's in the binary representation of k equals bigomega(k), the number of prime divisors of k (counted with multiplicity).

2, 6, 9, 10, 28, 33, 34, 42, 44, 50, 52, 54, 60, 65, 70, 76, 90, 98, 129, 135, 138, 148, 150, 156, 164, 184, 198, 204, 210, 225, 228, 232, 261, 266, 268, 273, 290, 292, 294, 297, 306, 308, 322, 330, 340, 344, 385, 388, 390, 405, 424, 440, 468, 486, 496, 504

Offset: 1

Jason Earls, Jun 07 2002

A115156 is a subsequence: A001222(A115156(n)) = A000120(A115156(n)) = n. - Reinhard Zumkeller, Jan 14 2006

			232 is a term because 232 = 11101000_2 and 232 = 2^3*29.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A000120, A001222, A071594, A115156.

fQ[n_] := Count[IntegerDigits[n, 2], 1] == Plus @@ Last /@ FactorInteger@n; Select[ Range@517, fQ[ # ] &] (* Robert G. Wilson v, Jan 18 2006 *)
Select[Range[600],Count[IntegerDigits[#,2],1]==PrimeOmega[#]&] (* Harvey P. Dale, Mar 07 2019 *)

A113758 a(n) is the least number having sum of digits n in base 10 and also exactly n prime factors (counted with multiplicity).

Original entry on oeis.org

10001, 12, 40, 32, 240, 3040, 2240, 1152, 6400, 12800, 21504, 440320, 2140160, 172032, 4710400, 1802240, 1327104, 20316160, 40632320, 17301504, 152043520, 602931200, 138412032, 117440512, 3607101440, 1132462080, 51204063232, 3355443200, 35232153600, 202400333824, 102005473280

Offset: 2

Giovanni Resta, Jan 18 2006

			a(2)=10001 since 1+0+0+0+1=2 and 10001=73*137 has 2 prime factors.
a(3)=12 since 1+2=3 and 12=2*2*3 has 3 prime factors.

Cf. A115156.

Lk[n_] := Block[{k = 2}, While[n != Plus @@ IntegerDigits[k] || n != Plus @@ (Transpose[FactorInteger@k][[2]]), k++ ]; k]; L = {}; Do[v = Lk[n]; Print[{n, v}]; AppendTo[L, v], {n, 2, 13}]; L

a(23)-a(28) from Donovan Johnson, Nov 15 2009

a(29)-a(32) from Giovanni Resta, Mar 21 2017

cp's OEIS Frontend

A071814 Numbers k such that the number of 1's in the binary representation of k equals bigomega(k), the number of prime divisors of k (counted with multiplicity).

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