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A217895 Sum of d/Gpf(d) for all divisors d of n, with Gpf(d) the greatest prime factor of d. 1
1, 2, 2, 4, 2, 5, 2, 8, 5, 5, 2, 11, 2, 5, 6, 16, 2, 14, 2, 11, 6, 5, 2, 23, 7, 5, 14, 11, 2, 17, 2, 32, 6, 5, 8, 32, 2, 5, 6, 23, 2, 17, 2, 11, 18, 5, 2, 47, 9, 20, 6, 11, 2, 41, 8, 23, 6, 5, 2, 39, 2, 5, 18, 64, 8, 17, 2, 11, 6, 23, 2, 68, 2, 5, 26, 11, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= n (see Proposition 5.2 in Girard's paper, link below).

a(p) = 2, when p is prime.

LINKS

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

Benjamin Girard, On a combinatorial problem of Erdos, Kleitman and Lemke, arXiv:1010.5042 [math.CO], 2010-2012.

Benjamin Girard, On a combinatorial problem of Erdos, Kleitman and Lemke, Advances in Mathematics 231, 3-4 (2012) 1843-1857.

EXAMPLE

The divisors of 6 are : 1, 2, 3, 6; so a(6)=1/gpf(1)+2/gpf(2)+3/gpf(3)+6/gpf(6) = 1/1 + 2/2 + 3/3 + 6/3 = 5.

MATHEMATICA

a[n_] := Sum[d/FactorInteger[d][[-1, 1]], {d, Divisors[n]}];

Array[a, 80] (* Jean-Fran├žois Alcover, Sep 26 2018 *)

PROG

(PARI) gpf(n) = {if (n==1, return (1), return (vecmax(factor(n)[, 1]))); }

a(n)= { my(d = divisors(n)); sum(j=1, length(d), d[j]/gpf(d[j])); } \\ revised by Michel Marcus, Sep 26 2018

CROSSREFS

Cf. A052126 (Mobius transform).

Sequence in context: A056148 A304442 A057567 * A328720 A005128 A187782

Adjacent sequences:  A217892 A217893 A217894 * A217896 A217897 A217898

KEYWORD

nonn

AUTHOR

Michel Marcus, Oct 14 2012

STATUS

approved

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Last modified September 19 10:41 EDT 2020. Contains 337178 sequences. (Running on oeis4.)