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A328957
Numbers k such that sigma_0(k) != omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
6
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 36, 37, 41, 42, 43, 47, 49, 53, 59, 61, 64, 66, 67, 70, 71, 72, 73, 78, 79, 81, 83, 89, 97, 100, 101, 102, 103, 105, 107, 108, 109, 110, 113, 114, 120, 121, 125, 127, 128, 130, 131, 137
OFFSET
1,2
LINKS
FORMULA
A000005(a(n)) != A001222(a(n)) * A001221(a(n)).
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
9: {2,2}
11: {5}
13: {6}
16: {1,1,1,1}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
30: {1,2,3}
31: {11}
32: {1,1,1,1,1}
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
Nonzeros of A328958.
The complement is A328956.
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: A357864 A331912 A326848 * A030230 A366914 A089352
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 01 2019
STATUS
approved