|
|
A028234
|
|
If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = n/p_1^e_1, with a(1) = 1.
|
|
151
|
|
|
1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 5, 1, 1, 9, 1, 5, 7, 11, 1, 3, 1, 13, 1, 7, 1, 15, 1, 1, 11, 17, 7, 9, 1, 19, 13, 5, 1, 21, 1, 11, 5, 23, 1, 3, 1, 25, 17, 13, 1, 27, 11, 7, 19, 29, 1, 15, 1, 31, 7, 1, 13, 33, 1, 17, 23, 35, 1, 9, 1, 37, 25, 19, 11, 39, 1, 5, 1, 41, 1, 21
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
Together with A067029 is useful for defining sequences that are multiplicative with a(p^e) = f(e), as recurrences of the form: a(1) = 1 and for n > 1, a(n) = f(A067029(n)) * a(A028234(n)). - Antti Karttunen, May 29 2017
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Sum_{k>=0} A005867(k)/(prime(k+1)*(prime(k+1)+1)*A002110(k)) = 0.114813... . - Amiram Eldar, Nov 19 2022
|
|
MATHEMATICA
|
a[n_] := n / Power @@ First[FactorInteger[n]]; Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Jun 12 2012 *)
|
|
PROG
|
(Haskell)
(PARI) a(n) = {my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); } \\ Michel Marcus, Feb 11 2016
(Python)
from sympy import factorint
def a(n):
f = factorint(n)
return 1 if n==1 else n/(min(f)**f[min(f)]) # Indranil Ghosh, May 12 2017
(GAP) a := List(List(List(List([1..10^3], Factors), Collected), i -> i[1]), j -> j[1]^j[2]);;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|