A328956 Numbers k such that sigma_0(k) = omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 68, 69, 74, 75, 76, 77, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 104, 106, 111, 112, 115, 116, 117

Offset: 1

Author

Gus Wiseman, Nov 01 2019

Keywords

• nonn

Comments

First differs from A084227 in having 60.

Examples

			The sequence of terms together with their prime indices begins:
   6: {1,2}
  10: {1,3}
  12: {1,1,2}
  14: {1,4}
  15: {2,3}
  18: {1,2,2}
  20: {1,1,3}
  21: {2,4}
  22: {1,5}
  24: {1,1,1,2}
  26: {1,6}
  28: {1,1,4}
  33: {2,5}
  34: {1,7}
  35: {3,4}
  38: {1,8}
  39: {2,6}
  40: {1,1,1,3}
  44: {1,1,5}
  45: {2,2,3}
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Zeros of A328958.

The complement is A328957.

Prime signature is A124010.

Omega-sequence is A323023.

omega(n) * Omega(n) is A113901(n).

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

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

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

Cf. A000040, A005117, A060687, A070175, A090858, A112798, A303555, A320632, A328960, A328961, A328962, A328963, A328964, A328965.

Programs

Mathematica

Select[Range[100],DivisorSigma[0,#]==PrimeOmega[#]*PrimeNu[#]&]

PARI

is(k) = {my(f = factor(k)); numdiv(f) == omega(f) * bigomega(f);} \\ Amiram Eldar, Jul 28 2024

Formula

A000005(a(n)) = A001222(a(n)) * A001221(a(n)).