A188654 Numbers k such that the maximum exponent in its prime factorization does not equal the number of positive exponents (A051903(k) <> A001221(k)).

4, 6, 8, 9, 10, 14, 15, 16, 21, 22, 24, 25, 26, 27, 30, 32, 33, 34, 35, 38, 39, 40, 42, 46, 48, 49, 51, 54, 55, 56, 57, 58, 60, 62, 64, 65, 66, 69, 70, 72, 74, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 96, 102, 104, 105, 106, 108, 110, 111

Offset: 1

Author

Reinhard Zumkeller, May 03 2013

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A212166 (complement), A225230.

Union of A212164 and A212168.

Programs

Haskell

import Data.List (findIndices)
a188654 n = a188654_list !! (n-1)
a188654_list = map (+ 1) $ findIndices (/= 0) a225230_list

Mathematica

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

PARI

is(k) = {my(e = factor(k)[, 2]); #e && vecmax(e) != #e;} \\ Amiram Eldar, Sep 08 2024

Formula

A051903(n) <> A001221(n);

A225230(a(n)) <> 0.