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%I #4 Sep 08 2019 12:59:26
%S 6,10,14,26,34,62,82,122,142,146,202,206,226,254,334,346,362,394,446,
%T 542,562,566,586,734,766,794,842,926,934,982,1046,1126,1286,1294,1346,
%U 1382,1514,1546,1594,1622,1654,1706,1766,1906,1934
%N Composite numbers for which the second elementary symmetric function of divisors (s2) is prime.
%C Terms in A119616 are always prime if n is prime p and s2(p)=p, hence it is interesting to find composite numbers for which s2 is also prime. Relative values of s2 are: s2=47,97,163,457,733,2203,3733,7993,10723,11317,21313,22147,26557,33403,57283,61417,67153,79393,101467,149323,160453,162727,174337,272683,296827,318793,358273,432907,440383,486583,551767,639007,832687,843043,911917,961183,1152913,1202017,1277593,1322743,1375303,1462897,1567327,1824997,1878883. Otherwise the sequence s2 gives numbers which appear in A119616 at least twice (and conjecture is that exactly twice).
%t dv:=Divisors[n];le:=Length[dv];re=Reap[Do[If[ !PrimeQ[n],su=Sum[dv[[i]]*dv[[i+j]],{i,1,le-1},{j,1,le-i}];If[PrimeQ[su],Sow[{n,su}]]],{n,2,2000}]][[2,1]]
%Y Cf. A119616.
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 08 2006