A187042 Numbers the expansion of which over distinct terms of A050376 contains the same number of primes and perfect squares.

8, 12, 18, 20, 27, 28, 32, 44, 45, 48, 50, 52, 63, 68, 75, 76, 80, 92, 98, 99, 112, 116, 117, 124, 125, 147, 148, 153, 162, 164, 171, 172, 175, 176, 188, 207, 208, 212, 216, 236, 242, 243, 244, 245, 261, 268, 272, 275, 279, 284, 292, 304, 316, 325, 332, 333, 338

Offset: 1

Author

Vladimir Shevelev, Mar 02 2011

Keywords

• nonn

Comments

The sequence does not contain squarefree numbers or perfect squares.

Initially the sequence matches A378494 (the intersection of A000379 and A026424). The first differences are the absence here of 120 and 168 and the inclusion here of 216. - Peter Munn, Jul 13 2024 (edited by Paolo Xausa, Nov 29 2024).

Examples

			147 and 216 are in the sequence, since their expansions over distinct terms of A050376 are 3*49 and 2*3*4*9 respectively. Thus the expansion of 147 contains one prime and one perfect square, while the expansion of 216 contains two primes and two perfect squares.
		

Links

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

Crossrefs

Cf. A050376, A187039, A378494.

Programs

Mathematica

aQ[n_] := Total @ (d = IntegerDigits[Last /@ FactorInteger[n], 2])[[;; , -1]] == Total @ Flatten @d / 2; Select[Range[350], aQ] (* Amiram Eldar, Oct 01 2019 *)

Extensions

a(28)=153 inserted and more terms added by Amiram Eldar, Oct 01 2019