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

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, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76

Offset: 1

Author

Reinhard Zumkeller, Feb 18 2012

Keywords

• nonn

Comments

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

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

Links

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

Crossrefs

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

Programs

Haskell

a207481 n = a207481_list !! (n-1)
a207481_list = [x | x <- [1..], and $ zipWith (<=)
                    (map toInteger $ a124010_row x) (a027748_row x) ]

Mathematica

okQ[n_] := AllTrue[FactorInteger[n], #[[2]] <= #[[1]]&];
Select[Range[100], okQ] (* Jean-François Alcover, Jun 08 2016 *)