A336359 Numbers k for which bigomega(sigma(k)) < bigomega(k), where bigomega (A001222) gives the number of prime factors with multiplicity, and sigma (A000203) gives the sum of divisors.

4, 8, 9, 16, 18, 25, 32, 36, 48, 50, 64, 72, 80, 81, 96, 100, 112, 128, 144, 160, 162, 176, 180, 192, 196, 200, 208, 225, 240, 243, 256, 272, 288, 289, 300, 304, 320, 324, 360, 384, 392, 400, 405, 416, 432, 441, 448, 450, 464, 468, 484, 486, 512, 576, 578, 592, 600, 624, 625, 640, 648, 656, 676, 688, 704, 720, 729, 768

Offset: 1

Author

Antti Karttunen, Jul 20 2020

Keywords

• nonn

Comments

Numbers k such that A058063(k) < A001222(k).

If terms x and y are present and gcd(x,y) = 1, then x*y is present also. This follows because both A001222 and A058063 are additive sequences, their difference A336386 is also.

Links

• Dumitru Damian, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A001222, A058063.

Cf. A336356 (characteristic function), A336360 (complement).

Positions of negative terms in A336386.

Programs

Mathematica

Select[Range[800],PrimeOmega[DivisorSigma[1,#]]Harvey P. Dale, Apr 02 2023 *)

PARI

isA336359(n) = (bigomega(sigma(n))
				

SageMath

b=sloane.A001222; [n for n in range(2,10^3) if b(sigma(n))Dumitru Damian, Nov 18 2021