A372781 Odd numbers k such that A001221(k) < A001221(A003958(k)).

7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 93, 97, 101, 103, 107, 109, 113, 121, 127, 129, 131, 137, 139, 143, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181, 183, 191, 193, 197, 199, 201, 203, 209, 211, 213, 215, 217, 223

Offset: 1

Author

Mike Jones, Jul 04 2024

Keywords

• nonn

Examples

			31 is in the sequence because 31 = 31^1, so omega(31) = 1, but (31 - 1)^1 = 30^1 = 2^1 * 3^1 * 5^1, so omega(30) = 3, and 1 < 3.
		

Crossrefs

Cf. A001221, A003958, A005408, A138889.

Programs

Maple

q:= n-> (f-> n::odd and f(n) nops(ifactors(k)[2])):
select(q, [$1..333])[];  # Alois P. Heinz, Jul 04 2024

Mathematica

f[p_, e_] := (p - 1)^e; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[3, 1000, 2], PrimeNu[#] < PrimeNu[s[#]] &] (* Amiram Eldar, Jul 04 2024 *)