A255585 Composite numbers k such that Sum_{i=1..t-1} d(i+1)/d(i) is prime, where d(1), ..., d(t) are the divisors of k in ascending order.

50, 98, 108, 242, 338, 375, 578, 1029, 1058, 1458, 1922, 2738, 3072, 3362, 3993, 4418, 5618, 7442, 8978, 9216, 10658, 13778, 14739, 18818, 20402, 20577, 21218, 22898, 26985, 31250, 34322, 45602, 46875, 49298, 55778, 58564, 59858, 72962, 73167, 74498, 78732

Offset

1,1

Comments

Subsequence of A255586.

The corresponding primes are 11, 13, 17, 17, 19, 17, 23, 19, 29, 23, 37, 43, 31, 47, 23, 53, 59, 67, 73, 43, 79, 89, 29, 103, 107, 31, 109, 113, 31, 29, 137, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..150 from Harvey P. Dale)

Example

98 is in the sequence because the divisors of 98 are {1, 2, 7, 14, 49, 98} and 2/1 + 7/2 + 14/7 + 49/14 + 98/49 = 13 is prime.

Mathematica

lst={}; Do[s=0; Do[s=s+Divisors[n][[i+1]]/Divisors[n][[i]], {i, 1, Length[Divisors[n]]-1}]; If[PrimeQ[s]&&!PrimeQ[n], AppendTo[lst, n]], {n, 80000}]; lst
compQ[n_]:=Module[{d=Divisors[n]}, CompositeQ[n]&&PrimeQ[Total[ Rest[d]/ Most[d]]]]; Select[Range[80000], compQ] (* Harvey P. Dale, Sep 03 2015 *)

Crossrefs

Cf. A085085, A085091, A255576, A255586.

Sequence in context: A228953 A335480 A375137 * A260901 A090997 A141757

Adjacent sequences: A255582 A255583 A255584 * A255586 A255587 A255588

Keyword

nonn

Author

Michel Lagneau, Feb 27 2015

Status

approved