|
| |
|
|
A375142
|
|
Numbers whose powerful part (A057521) is a power of a squarefree number that is larger than 1 (A072777).
|
|
3
|
|
|
|
4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 68, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 104, 112, 116, 117, 120, 121, 124, 125, 126, 128, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Subsequence of A013929 and first differs from it at n = 27: A013929(27) = 72 = 2^3 * 3^2 is not a term of this sequence.
Numbers whose prime factorization has one distinct exponent that does not equal 1.
Numbers that are a product of a squarefree number (A005117) and a power of a different squarefree number that is not squarefree.
The asymptotic density of this sequence is Sum_{k>=2} (d(k)-1)/zeta(2) = 0.36113984820338109927..., where d(k) = zeta(k) * Product_{p prime} (1 + Sum_{i=k+1..2*k-1} (-1)^i/p^i), if k is even, and d(k) = (zeta(2*k)/zeta(k)) * Product_{p prime} (1 + 2/p^k + Sum_{i=k+1..2*k-1} (-1)^(i+1)/p^i) if k is odd > 1.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
12 = 2^2 * 3 is a term because its powerful part, 4 = 2^2, is a power of a squarefree number, 2, that is larger than 1.
|
|
|
MATHEMATICA
|
q[n_] := Count[Union[FactorInteger[n][[;; , 2]]], _?(# > 1 &)] == 1; Select[Range[200], q]
|
|
|
PROG
|
(PARI) is(k) = {my(e = select(x -> (x > 1), Set(factor(k)[, 2]))); #e == 1; }
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
