cp's OEIS Frontend

A212164 Numbers k such that the maximum exponent in its prime factorization is greater than the number of positive exponents (A051903(k) > A001221(k)).

%I A212164 #18 Sep 09 2024 09:36:58
%S A212164 4,8,9,16,24,25,27,32,40,48,49,54,56,64,72,80,81,88,96,104,108,112,
%T A212164 121,125,128,135,136,144,152,160,162,169,176,184,189,192,200,208,216,
%U A212164 224,232,240,243,248,250,256,272,288,289,296,297,304,320,324,328,336
%N A212164 Numbers k such that the maximum exponent in its prime factorization is greater than the number of positive exponents (A051903(k) > A001221(k)).
%D A212164 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
%H A212164 Reinhard Zumkeller, <a href="/A212164/b212164.txt">Table of n, a(n) for n = 1..10000</a>
%H A212164 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A212164 Primefan, <a href="http://primefan.tripod.com/500factored.html">The First 2500 Integers Factored</a> (first of 5 pages).
%F A212164 A225230(a(n)) < 0; A050326(a(n)) = 0. - _Reinhard Zumkeller_, May 03 2013
%e A212164 40 = 2^3*5^1 has 2 distinct prime factors, hence, 2 positive exponents in its prime factorization (namely, 3 and 1, although the 1 is often left implicit).   2 is less than the maximal exponent in 40's prime factorization, which is 3. Therefore, 40 belongs to the sequence.
%t A212164 okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] > Length[f]]; Select[Range[1000], okQ] (* _T. D. Noe_, May 24 2012 *)
%o A212164 (Haskell)
%o A212164 import Data.List (elemIndices)
%o A212164 a212164 n = a212164_list !! (n-1)
%o A212164 a212164_list = map (+ 1) $ findIndices (< 0) a225230_list
%o A212164 -- _Reinhard Zumkeller_, May 03 2013
%o A212164 (PARI) is(k) = {my(e = factor(k)[, 2]); #e && vecmax(e) > #e;} \\ _Amiram Eldar_, Sep 08 2024
%Y A212164 Complement of A212167.
%Y A212164 See also A212165, A212166, A212168.
%Y A212164 Cf. A001221, A050326, A051903, A225230.
%Y A212164 Subsequence of A188654.
%K A212164 nonn,easy
%O A212164 1,1
%A A212164 _Matthew Vandermast_, May 22 2012