cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A119623 Composite numbers for which the second elementary symmetric function of divisors (s2) is prime.

This page as a plain text file.
%I A119623 #4 Sep 08 2019 12:59:26
%S A119623 6,10,14,26,34,62,82,122,142,146,202,206,226,254,334,346,362,394,446,
%T A119623 542,562,566,586,734,766,794,842,926,934,982,1046,1126,1286,1294,1346,
%U A119623 1382,1514,1546,1594,1622,1654,1706,1766,1906,1934
%N A119623 Composite numbers for which the second elementary symmetric function of divisors (s2) is prime.
%C A119623 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 A119623 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 A119623 Cf. A119616.
%K A119623 nonn
%O A119623 1,1
%A A119623 _Zak Seidov_, Jun 08 2006