cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A188654 #21 Sep 08 2024 13:47:10
%S A188654 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 A188654 48,49,51,54,55,56,57,58,60,62,64,65,66,69,70,72,74,77,78,80,81,82,84,
%U A188654 85,86,87,88,90,91,93,94,95,96,102,104,105,106,108,110,111
%N A188654 Numbers k such that the maximum exponent in its prime factorization does not equal the number of positive exponents (A051903(k) <> A001221(k)).
%H A188654 Reinhard Zumkeller, <a href="/A188654/b188654.txt">Table of n, a(n) for n = 1..10000</a>
%F A188654 A051903(n) <> A001221(n);
%F A188654 A225230(a(n)) <> 0.
%t A188654 q[n_] := Module[{e = FactorInteger[n][[;;, 2]]}, Max[e] != Length[e]]; q[1] = False; Select[Range[120], q] (* _Amiram Eldar_, Sep 08 2024 *)
%o A188654 (Haskell)
%o A188654 import Data.List (findIndices)
%o A188654 a188654 n = a188654_list !! (n-1)
%o A188654 a188654_list = map (+ 1) $ findIndices (/= 0) a225230_list
%o A188654 (PARI) is(k) = {my(e = factor(k)[, 2]); #e && vecmax(e) != #e;} \\ _Amiram Eldar_, Sep 08 2024
%Y A188654 Cf. A001221, A212166 (complement), A225230.
%Y A188654 Union of A212164 and A212168.
%K A188654 nonn,easy
%O A188654 1,1
%A A188654 _Reinhard Zumkeller_, May 03 2013