A073083 Numbers n such that sum k/d(k) is an integer, where d(k) is the k-th divisor of n (the divisors of n are in decreasing order).

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

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*k-3)*13 and 13^(17*k-7)*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