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

1,1

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

Mathematica

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

Prog

(PARI) isA336359(n) = (bigomega(sigma(n))<bigomega(n));
(SageMath) b=sloane.A001222; [n for n in range(2, 10^3) if b(sigma(n))<b(n)] # Dumitru Damian, Nov 18 2021

Crossrefs

Cf. A000203, A001222, A058063.

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

Positions of negative terms in A336386.

Sequence in context: A255586 A034038 A069265 * A371013 A359680 A003679

Adjacent sequences: A336356 A336357 A336358 * A336360 A336361 A336362

Keyword

nonn

Author

Antti Karttunen, Jul 20 2020

Status

approved