A212164 - OEIS

A212164

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

4, 8, 9, 16, 24, 25, 27, 32, 40, 48, 49, 54, 56, 64, 72, 80, 81, 88, 96, 104, 108, 112, 121, 125, 128, 135, 136, 144, 152, 160, 162, 169, 176, 184, 189, 192, 200, 208, 216, 224, 232, 240, 243, 248, 250, 256, 272, 288, 289, 296, 297, 304, 320, 324, 328, 336

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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.

LINKS

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

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Primefan, The First 2500 Integers Factored (first of 5 pages).

FORMULA

A225230(a(n)) < 0; A050326(a(n)) = 0. - Reinhard Zumkeller, May 03 2013

EXAMPLE

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.

MATHEMATICA

okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] > Length[f]]; Select[Range[1000], okQ] (* T. D. Noe, May 24 2012 *)

PROG

(Haskell)

import Data.List (elemIndices)

a212164 n = a212164_list !! (n-1)

a212164_list = map (+ 1) $ findIndices (< 0) a225230_list

-- Reinhard Zumkeller, May 03 2013

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

CROSSREFS

Complement of A212167.