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

Author

Michel Lagneau, Feb 27 2015

Keywords

• nonn

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, ...

Examples

			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.
		

Links

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

Crossrefs

Cf. A085085, A085091, A255576, A255586.

Programs

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 *)