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

36, 60, 84, 90, 100, 126, 132, 140, 150, 156, 196, 198, 204, 220, 225, 228, 234, 260, 276, 294, 306, 308, 315, 340, 342, 348, 350, 364, 372, 380, 414, 441, 444, 460, 476, 484, 490, 492, 495, 516, 522, 525, 532, 550, 558, 564, 572, 580, 585, 620, 636, 644, 650

Offset: 1

Author

Gus Wiseman, Nov 02 2019

Keywords

• nonn

Comments

These appear to be all positive integers with prime signature (2,2), (2,1,1), (1,2,1), or (1,1,2).

Examples

			The sequence of terms together with their prime indices begins:
   36: {1,1,2,2}
   60: {1,1,2,3}
   84: {1,1,2,4}
   90: {1,2,2,3}
  100: {1,1,3,3}
  126: {1,2,2,4}
  132: {1,1,2,5}
  140: {1,1,3,4}
  150: {1,2,3,3}
  156: {1,1,2,6}
  196: {1,1,4,4}
  198: {1,2,2,5}
  204: {1,1,2,7}
  220: {1,1,3,5}
  225: {2,2,3,3}
  228: {1,1,2,8}
  234: {1,2,2,6}
  260: {1,1,3,6}
  276: {1,1,2,9}
		

Crossrefs

Prime signature is A124010.

(omega(n) - 1) * nu(n) is A307409(n).

sigma_0(n) - omega(n) * nu(n) is A328958(n).

sigma_0(n) - 2 - (omega(n) - 1) * nu(n) is A328959(n).

Cf. A000005, A001221, A001222, A113901, A320632, A328956, A328960, A328963, A328965.

Programs

Mathematica

Select[Range[100],DivisorSigma[0,#]-3==(PrimeOmega[#]-1)*PrimeNu[#]&]

Formula

A000005(a(n)) - 3 = (A001222(a(n)) - 1) * A001221(a(n)).