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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.
5
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
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. A336356 (characteristic function), A336360 (complement).
Positions of negative terms in A336386.
Sequence in context: A255586 A034038 A069265 * A371013 A359680 A003679
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 20 2020
STATUS
approved