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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.
2

%I #16 Jul 07 2022 06:43:43

%S 50,98,108,242,338,375,578,1029,1058,1458,1922,2738,3072,3362,3993,

%T 4418,5618,7442,8978,9216,10658,13778,14739,18818,20402,20577,21218,

%U 22898,26985,31250,34322,45602,46875,49298,55778,58564,59858,72962,73167,74498,78732

%N 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.

%C Subsequence of A255586.

%C 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, ...

%H Amiram Eldar, <a href="/A255585/b255585.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..150 from Harvey P. Dale)

%e 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.

%t 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

%t compQ[n_]:=Module[{d=Divisors[n]},CompositeQ[n]&&PrimeQ[Total[ Rest[d]/ Most[d]]]]; Select[Range[80000],compQ] (* _Harvey P. Dale_, Sep 03 2015 *)

%Y Cf. A085085, A085091, A255576, A255586.

%K nonn

%O 1,1

%A _Michel Lagneau_, Feb 27 2015