|
|
A365889
|
|
Numbers k whose least prime divisor divides its exponent in the prime factorization of k.
|
|
4
|
|
|
4, 12, 16, 20, 27, 28, 36, 44, 48, 52, 60, 64, 68, 76, 80, 84, 92, 100, 108, 112, 116, 124, 132, 135, 140, 144, 148, 156, 164, 172, 176, 180, 188, 189, 192, 196, 204, 208, 212, 220, 228, 236, 240, 244, 252, 256, 260, 268, 272, 276, 284, 292, 297, 300, 304, 308
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The asymptotic density of terms with least prime factor prime(n) (within all the positive integers) is d(n) = ((prime(n)-1)/(prime(n)*(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) = 1/6, 1/78, 1/11715, 4/14411985 and 8/10984499318485.
The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.17957281768342725732... .
|
|
LINKS
|
|
|
EXAMPLE
|
4 = 2^2 is a term since its least prime factor, 2, divides its exponent, 2.
16 = 2^4 is a term since its least prime factor, 2, divides its exponent, 4.
|
|
MATHEMATICA
|
q[n_] := Divisible @@ Reverse[FactorInteger[n][[1]]]; Select[Range[2, 400], q]
|
|
PROG
|
(PARI) is(n) = {my(f = factor(n)); n > 1 && !(f[1, 2] % f[1, 1]); }
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|