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A365886
Numbers k whose least prime divisor is smaller than its exponent in the prime factorization of k.
3
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 81, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 243, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 405, 408, 416
OFFSET
1,1
COMMENTS
First differs from A185359 at n = 22.
Numbers k such that A020639(k) < A051904(k).
The asymptotic density of terms with least prime factor prime(n) (within all the positive integers) is d(n) = (1/prime(n)^(prime(n)+1)) * Product_{k=1..(n-1)} (1-1/prime(k)). For example, for n = 1, 2, 3, 4 and 5, d(n) = 1/8, 1/162, 1/46875, 4/86472015 and 8/109844993185235.
The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.13119421909731920416... .
LINKS
EXAMPLE
8 = 2^3 is a term since its least prime factor, 2, is smaller than its exponent, 3.
MATHEMATICA
q[n_] := Less @@ FactorInteger[n][[1]]; Select[Range[2, 420], q]
PROG
(PARI) is(n) = {my(f = factor(n)); n > 1 && f[1, 1] < f[1, 2]; }
CROSSREFS
Subsequences: A008590 \ {0}, A365887, A365888.
Subsequence of A185359.
Sequence in context: A277780 A044893 A185359 * A022144 A181390 A008590
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved