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A322448 Numbers whose prime factorization contains at least one composite exponent. 3
16, 48, 64, 80, 81, 112, 144, 162, 176, 192, 208, 240, 256, 272, 304, 320, 324, 336, 368, 400, 405, 432, 448, 464, 496, 512, 528, 560, 567, 576, 592, 624, 625, 648, 656, 688, 704, 720, 729, 752, 768, 784, 810, 816, 832, 848, 880, 891, 912, 944, 960, 976, 1008 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^4 + Sum_{q prime >= 5} 1/p^q - 1/p^(q-1)) = 0.05328066264472198953... (using the method of Shevelev, 2016). - Amiram Eldar, Nov 08 2020

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Vladimir Shevelev, A fast computation of density of exponentially S-numbers, arXiv:1602.04244 [math.NT], 2016.

EXAMPLE

16 = 2^4 is a term because 4 is a composite exponent here.

MAPLE

a:= proc(n) option remember; local k; for k from 1+

      `if`(n=1, 0, a(n-1)) while andmap(i-> i[2]=1 or

       isprime(i[2]), ifactors(k)[2]) do od; k

    end:

seq(a(n), n=1..70);

MATHEMATICA

Select[Range[1000], AnyTrue[FactorInteger[#][[;; , 2]], CompositeQ] &] (* Amiram Eldar, Nov 08 2020 *)

PROG

(PARI) isok(m) = #select(x->((x>1) && !isprime(x)), factor(m)[, 2]) > 0; \\ Michel Marcus, Dec 02 2020

CROSSREFS

Cf. A002808, A322449.

Sequence in context: A223440 A223402 A260985 * A264164 A045047 A239344

Adjacent sequences:  A322445 A322446 A322447 * A322449 A322450 A322451

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 08 2018

STATUS

approved

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Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)