|
|
A217579
|
|
a(1) = 1; for n > 1, a(n) = max(d*lpf(d) : d|n, d > 1), where lpf is the least prime factor function (A020639).
|
|
1
|
|
|
1, 4, 9, 8, 25, 12, 49, 16, 27, 25, 121, 24, 169, 49, 45, 32, 289, 36, 361, 40, 63, 121, 529, 48, 125, 169, 81, 56, 841, 60, 961, 64, 121, 289, 175, 72, 1369, 361, 169, 80, 1681, 84, 1849, 121, 135, 529, 2209, 96, 343, 125, 289, 169, 2809, 108, 275, 112, 361
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Function considered by Schinzel and Szekeres in connection with a sieve problem.
|
|
REFERENCES
|
A. Schinzel, G. Szekeres, Sur un problème de M. Paul Erdős, Acta Sci. Math. Szeged 20 (1959), 221-229.
|
|
LINKS
|
|
|
EXAMPLE
|
The divisors of 6 greater than 1 are : 2, 3, 6. The maximum of (2*A020639(2), 3*A020639(3), 6*A020639(6)) is max (2*2, 3*3, 6*2) is 6*2=12, so a(6)=12.
|
|
MATHEMATICA
|
a[1]=1; a[n_] := Table[d FactorInteger[d][[1, 1]], {d, Rest[Divisors[n]]}] // Max; Array[a, 60] (* Jean-François Alcover, Sep 26 2018 *)
|
|
PROG
|
(PARI) spf(n) = vecmin(factor(n)[, 1]);
a(n) = if (n==1, 1, d = divisors(n); vecmax(vector(#d-1, k, d[k+1]*spf(d[k+1])))); \\ Michel Marcus, Mar 28 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|