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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.

%I A336359 #22 Apr 02 2023 16:57:28
%S A336359 4,8,9,16,18,25,32,36,48,50,64,72,80,81,96,100,112,128,144,160,162,
%T A336359 176,180,192,196,200,208,225,240,243,256,272,288,289,300,304,320,324,
%U A336359 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
%N 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.
%C A336359 Numbers k such that A058063(k) < A001222(k).
%C A336359 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.
%H A336359 Dumitru Damian, <a href="/A336359/b336359.txt">Table of n, a(n) for n = 1..20000</a>
%t A336359 Select[Range[800],PrimeOmega[DivisorSigma[1,#]]<PrimeOmega[#]&] (* _Harvey P. Dale_, Apr 02 2023 *)
%o A336359 (PARI) isA336359(n) = (bigomega(sigma(n))<bigomega(n));
%o A336359 (SageMath) b=sloane.A001222; [n for n in range(2,10^3) if b(sigma(n))<b(n)] # _Dumitru Damian_, Nov 18 2021
%Y A336359 Cf. A000203, A001222, A058063.
%Y A336359 Cf. A336356 (characteristic function), A336360 (complement).
%Y A336359 Positions of negative terms in A336386.
%K A336359 nonn
%O A336359 1,1
%A A336359 _Antti Karttunen_, Jul 20 2020