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Odd numbers k such that A001221(k) < A001221(A003958(k)).
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%I #29 Jul 06 2024 14:01:05

%S 7,11,13,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,77,79,83,89,93,

%T 97,101,103,107,109,113,121,127,129,131,137,139,143,149,151,155,157,

%U 161,163,167,169,173,179,181,183,191,193,197,199,201,203,209,211,213,215,217,223

%N Odd numbers k such that A001221(k) < A001221(A003958(k)).

%e 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.

%p q:= n-> (f-> n::odd and f(n)<f(mul((i[1]-1)^i[2],

%p i=ifactors(n)[2])))(k-> nops(ifactors(k)[2])):

%p select(q, [$1..333])[]; # _Alois P. Heinz_, Jul 04 2024

%t 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 *)

%Y Cf. A001221, A003958, A005408, A138889.

%K nonn

%O 1,1

%A _Mike Jones_, Jul 04 2024