

A073083


Numbers n such that sum k/d(k) is an integer, where d(k) is the kth divisor of n (the divisors of n are in decreasing order).


1



1, 10, 12, 24, 615, 4066, 7960, 30432, 49260, 133686, 440286, 1201644, 6640812, 126953125, 411106256, 1046704882, 11046706752, 44588839041
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OFFSET

1,2


COMMENTS

a(12) > 11*10^5.  Emeric Deutsch, Mar 05 2005
8*10^11 < a(19) <= 2343594361433 = 13^10*17. It seems that the numbers 5^(13*k3)*13 and 13^(17*k7)*17, for k > 0, are terms.  Giovanni Resta, Dec 06 2019


LINKS

Table of n, a(n) for n=1..18.


EXAMPLE

The divisors of 615 are [615,205,123,41,15,5,3,1] and 1/615+2/205+3/123+4/41+5/15+6/5+7/3+8/1 = 12 is an integer hence 615 is in the sequence.


MATHEMATICA

Select[Range[441000], IntegerQ[Total[Range[DivisorSigma[0, #]]/ Reverse[ Divisors[ #]]]]&] (* Harvey P. Dale, May 23 2019 *)


PROG

(MAGMA) [k:k in [1..500000]IsIntegral(&+[m/Reverse(Divisors(k))[m]:m in [1..#Divisors(k)]])]; // Marius A. Burtea, Dec 06 2019


CROSSREFS

Cf. A056538, A073082.
Sequence in context: A241177 A140972 A108901 * A129508 A015728 A080470
Adjacent sequences: A073080 A073081 A073082 * A073084 A073085 A073086


KEYWORD

nonn,more


AUTHOR

Benoit Cloitre, Aug 17 2002


EXTENSIONS

More terms from Emeric Deutsch, Mar 05 2005
a(12)a(17) from Lambert Klasen (lambert.klasen(AT)gmx.net), Jul 15 2005
a(18) from Giovanni Resta, Dec 06 2019


STATUS

approved



