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%I #12 Jul 02 2021 11:30:39
%S 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,38,39,40,44,45,46,48,50,
%T 51,52,54,55,56,57,58,60,62,63,65,68,69,74,75,76,77,80,82,84,85,86,87,
%U 88,90,91,92,93,94,95,96,98,99,104,106,111,112,115,116,117
%N Numbers k such that sigma_0(k) = omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
%C First differs from A084227 in having 60.
%F A000005(a(n)) = A001222(a(n)) * A001221(a(n)).
%e The sequence of terms together with their prime indices begins:
%e 6: {1,2}
%e 10: {1,3}
%e 12: {1,1,2}
%e 14: {1,4}
%e 15: {2,3}
%e 18: {1,2,2}
%e 20: {1,1,3}
%e 21: {2,4}
%e 22: {1,5}
%e 24: {1,1,1,2}
%e 26: {1,6}
%e 28: {1,1,4}
%e 33: {2,5}
%e 34: {1,7}
%e 35: {3,4}
%e 38: {1,8}
%e 39: {2,6}
%e 40: {1,1,1,3}
%e 44: {1,1,5}
%e 45: {2,2,3}
%t Select[Range[100],DivisorSigma[0,#]==PrimeOmega[#]*PrimeNu[#]&]
%Y Zeros of A328958.
%Y The complement is A328957.
%Y Prime signature is A124010.
%Y Omega-sequence is A323023.
%Y omega(n) * Omega(n) is A113901(n).
%Y (Omega(n) - 1) * omega(n) is A307409(n).
%Y sigma_0(n) - omega(n) * Omega(n) is A328958(n).
%Y sigma_0(n) - 2 - (Omega(n) - 1) * omega(n) is A328959(n).
%Y Cf. A000040, A005117, A060687, A070175, A090858, A112798, A303555, A320632, A328960, A328961, A328962, A328963, A328964, A328965.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 01 2019
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