A255586 Composite n such that Sum_{i=1..t-1} d(i+1)/d(i) is an integer, where d(1), ..., d(t) are the divisors of n in ascending order.

4, 8, 9, 16, 18, 25, 27, 32, 48, 49, 50, 64, 81, 98, 108, 121, 125, 128, 162, 169, 242, 243, 256, 289, 338, 343, 361, 375, 512, 529, 578, 625, 722, 729, 841, 961, 1024, 1029, 1058, 1250, 1331, 1369, 1458, 1681, 1682, 1849, 1920, 1922, 2048, 2187, 2197, 2209

Offset

1,1

Comments

The sequence is infinite because the powers of 2 (A000079) are in the sequence.

The prime powers with even exponents (A056798) are in the sequence.

The cubes of primes (A030078) are in the sequence.

The numbers of the form 2p^2 (A079704) with p prime are in the sequence.

The corresponding integers are 4, 6, 6, 8, 9, 10, 9, 10, 14, 14, 11, 12, 12, 13, 17, 22, 15, 14, 16, 26, 17, 15, 16, 34, 19, ...

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

18 is in the sequence because the divisors of 18 are {1, 2, 3, 6, 9, 18} and 2/1 + 3/2 + 6/3 + 9/6 + 18/9 = 9 is integer.

Mathematica

lst={}; Do[s=0; Do[s=s+Divisors[n][[i+1]]/Divisors[n][[i]], {i, 1, Length[Divisors[n]]-1}]; If[IntegerQ[s]&&!PrimeQ[n], AppendTo[lst, n]], {n, 2300}]; lst
Select[Range[2210], CompositeQ[#]&&IntegerQ[Total[#[[2]]/#[[1]]&/@Partition[ Divisors[ #], 2, 1]]]&] (* Harvey P. Dale, Jul 09 2019 *)

Crossrefs

Cf. A000079, A030078, A079704, A227993, A255585.

Sequence in context: A073539 A090779 A166402 * A034038 A069265 A336359

Adjacent sequences: A255583 A255584 A255585 * A255587 A255588 A255589

Keyword

nonn

Author

Michel Lagneau, Feb 27 2015

Status

approved