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A328956
Numbers k such that sigma_0(k) = omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
13
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
1,1
COMMENTS
First differs from A084227 in having 60.
LINKS
FORMULA
A000005(a(n)) = A001222(a(n)) * A001221(a(n)).
EXAMPLE
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}
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]==PrimeOmega[#]*PrimeNu[#]&]
PROG
(PARI) is(k) = {my(f = factor(k)); numdiv(f) == omega(f) * bigomega(f); } \\ Amiram Eldar, Jul 28 2024
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).
Sequence in context: A267114 A275665 A056760 * A084227 A299992 A237051
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 01 2019
STATUS
approved