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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

Altug Alkan, Table of n, a(n) for n = 1..10000

Pierre Mazet, Eric Saias, Etude du graphe divisoriel 4, arXiv:1803.10073 [math.NT], 2018. See p. 3.

G. Tenenbaum, Sur un problème de crible et ses applications, Annales scientifiques de l'École Normale Supérieure, 4ème série, tome 19, n°1, (1986), p.1-30.

G. Tenenbaum, Sur un problème de crible et ses applications. II. Corrigendum et étude du graphe divisoriel, Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 28 (1995) no. 2 , p. 115-127.

A. Weingartner, Integers with dense divisors, Journal of Number Theory,  Volume 108, Issue 1, September 2004, Pages 1-17.

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

Sequence in context: A318279 A065642 A285109 * A118585 A067666 A280286

Adjacent sequences:  A217576 A217577 A217578 * A217580 A217581 A217582

KEYWORD

nonn,look

AUTHOR

Michel Marcus, Oct 12 2012

STATUS

approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)