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A328961 Positive integers n such that sigma_0(n) - 3 = (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.

%I A328961 #5 Nov 03 2019 19:50:30
%S A328961 36,60,84,90,100,126,132,140,150,156,196,198,204,220,225,228,234,260,
%T A328961 276,294,306,308,315,340,342,348,350,364,372,380,414,441,444,460,476,
%U A328961 484,490,492,495,516,522,525,532,550,558,564,572,580,585,620,636,644,650
%N A328961 Positive integers n such that sigma_0(n) - 3 = (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.
%C A328961 These appear to be all positive integers with prime signature (2,2), (2,1,1), (1,2,1), or (1,1,2).
%F A328961 A000005(a(n)) - 3 = (A001222(a(n)) - 1) * A001221(a(n)).
%e A328961 The sequence of terms together with their prime indices begins:
%e A328961    36: {1,1,2,2}
%e A328961    60: {1,1,2,3}
%e A328961    84: {1,1,2,4}
%e A328961    90: {1,2,2,3}
%e A328961   100: {1,1,3,3}
%e A328961   126: {1,2,2,4}
%e A328961   132: {1,1,2,5}
%e A328961   140: {1,1,3,4}
%e A328961   150: {1,2,3,3}
%e A328961   156: {1,1,2,6}
%e A328961   196: {1,1,4,4}
%e A328961   198: {1,2,2,5}
%e A328961   204: {1,1,2,7}
%e A328961   220: {1,1,3,5}
%e A328961   225: {2,2,3,3}
%e A328961   228: {1,1,2,8}
%e A328961   234: {1,2,2,6}
%e A328961   260: {1,1,3,6}
%e A328961   276: {1,1,2,9}
%t A328961 Select[Range[100],DivisorSigma[0,#]-3==(PrimeOmega[#]-1)*PrimeNu[#]&]
%Y A328961 Prime signature is A124010.
%Y A328961 (omega(n) - 1) * nu(n) is A307409(n).
%Y A328961 sigma_0(n) - omega(n) * nu(n) is A328958(n).
%Y A328961 sigma_0(n) - 2 - (omega(n) - 1) * nu(n) is A328959(n).
%Y A328961 Cf. A000005, A001221, A001222, A113901, A320632, A328956, A328960, A328963, A328965.
%K A328961 nonn
%O A328961 1,1
%A A328961 _Gus Wiseman_, Nov 02 2019