A328961 - OEIS

%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