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