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A328956 Numbers k such that sigma_0(k) = omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.

%I A328956 #18 Jul 28 2024 10:08:03
%S A328956 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,38,39,40,44,45,46,48,50,
%T A328956 51,52,54,55,56,57,58,60,62,63,65,68,69,74,75,76,77,80,82,84,85,86,87,
%U A328956 88,90,91,92,93,94,95,96,98,99,104,106,111,112,115,116,117
%N A328956 Numbers k such that sigma_0(k) = omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
%C A328956 First differs from A084227 in having 60.
%H A328956 Amiram Eldar, <a href="/A328956/b328956.txt">Table of n, a(n) for n = 1..10000</a>
%F A328956 A000005(a(n)) = A001222(a(n)) * A001221(a(n)).
%e A328956 The sequence of terms together with their prime indices begins:
%e A328956    6: {1,2}
%e A328956   10: {1,3}
%e A328956   12: {1,1,2}
%e A328956   14: {1,4}
%e A328956   15: {2,3}
%e A328956   18: {1,2,2}
%e A328956   20: {1,1,3}
%e A328956   21: {2,4}
%e A328956   22: {1,5}
%e A328956   24: {1,1,1,2}
%e A328956   26: {1,6}
%e A328956   28: {1,1,4}
%e A328956   33: {2,5}
%e A328956   34: {1,7}
%e A328956   35: {3,4}
%e A328956   38: {1,8}
%e A328956   39: {2,6}
%e A328956   40: {1,1,1,3}
%e A328956   44: {1,1,5}
%e A328956   45: {2,2,3}
%t A328956 Select[Range[100],DivisorSigma[0,#]==PrimeOmega[#]*PrimeNu[#]&]
%o A328956 (PARI) is(k) = {my(f = factor(k)); numdiv(f) == omega(f) * bigomega(f);} \\ _Amiram Eldar_, Jul 28 2024
%Y A328956 Zeros of A328958.
%Y A328956 The complement is A328957.
%Y A328956 Prime signature is A124010.
%Y A328956 Omega-sequence is A323023.
%Y A328956 omega(n) * Omega(n) is A113901(n).
%Y A328956 (Omega(n) - 1) * omega(n) is A307409(n).
%Y A328956 sigma_0(n) - omega(n) * Omega(n) is A328958(n).
%Y A328956 sigma_0(n) - 2 - (Omega(n) - 1) * omega(n) is A328959(n).
%Y A328956 Cf. A000040, A005117, A060687, A070175, A090858, A112798, A303555, A320632, A328960, A328961, A328962, A328963, A328964, A328965.
%K A328956 nonn
%O A328956 1,1
%A A328956 _Gus Wiseman_, Nov 01 2019