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A207481 Numbers such that e <= p for all p^e in their prime factorization, p prime. 9

%I #19 Nov 24 2020 10:26:01

%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,27,28,

%T 29,30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,

%U 55,57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76

%N Numbers such that e <= p for all p^e in their prime factorization, p prime.

%C Proper subsequence of A047592, a(n) = A047592(n) for n <= 70.

%C The asymptotic density of this sequence is Product_{p prime} 1 - 1/p^(p+1) = 0.86414207232219778408... - _Amiram Eldar_, Nov 24 2020

%H Reinhard Zumkeller, <a href="/A207481/b207481.txt">Table of n, a(n) for n = 1..10000</a>

%t okQ[n_] := AllTrue[FactorInteger[n], #[[2]] <= #[[1]]&];

%t Select[Range[100], okQ] (* _Jean-François Alcover_, Jun 08 2016 *)

%o (Haskell)

%o a207481 n = a207481_list !! (n-1)

%o a207481_list = [x | x <- [1..], and $ zipWith (<=)

%o (map toInteger $ a124010_row x) (a027748_row x) ]

%Y Cf. A185359 (complement), A054743 (same construction, but with e > p)

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Feb 18 2012

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Last modified September 18 17:53 EDT 2024. Contains 376002 sequences. (Running on oeis4.)