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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.
6
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
1,1
COMMENTS
These appear to be all positive integers with prime signature (2,2), (2,1,1), (1,2,1), or (1,1,2).
FORMULA
A000005(a(n)) - 3 = (A001222(a(n)) - 1) * A001221(a(n)).
EXAMPLE
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}
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]-3==(PrimeOmega[#]-1)*PrimeNu[#]&]
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).
Sequence in context: A320632 A368832 A188633 * A335295 A287862 A066505
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 02 2019
STATUS
approved