A188654 - OEIS

%I #21 Sep 08 2024 13:47:10

%S 4,6,8,9,10,14,15,16,21,22,24,25,26,27,30,32,33,34,35,38,39,40,42,46,

%T 48,49,51,54,55,56,57,58,60,62,64,65,66,69,70,72,74,77,78,80,81,82,84,

%U 85,86,87,88,90,91,93,94,95,96,102,104,105,106,108,110,111

%N Numbers k such that the maximum exponent in its prime factorization does not equal the number of positive exponents (A051903(k) <> A001221(k)).

%H Reinhard Zumkeller, <a href="/A188654/b188654.txt">Table of n, a(n) for n = 1..10000</a>

%F A051903(n) <> A001221(n);

%F A225230(a(n)) <> 0.

%t q[n_] := Module[{e = FactorInteger[n][[;;, 2]]}, Max[e] != Length[e]]; q[1] = False; Select[Range[120], q] (* _Amiram Eldar_, Sep 08 2024 *)

%o (Haskell)

%o import Data.List (findIndices)

%o a188654 n = a188654_list !! (n-1)

%o a188654_list = map (+ 1) $ findIndices (/= 0) a225230_list

%o (PARI) is(k) = {my(e = factor(k)[, 2]); #e && vecmax(e) != #e;} \\ _Amiram Eldar_, Sep 08 2024

%Y Cf. A001221, A212166 (complement), A225230.

%Y Union of A212164 and A212168.

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, May 03 2013