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

6, 10, 14, 26, 34, 62, 82, 122, 142, 146, 202, 206, 226, 254, 334, 346, 362, 394, 446, 542, 562, 566, 586, 734, 766, 794, 842, 926, 934, 982, 1046, 1126, 1286, 1294, 1346, 1382, 1514, 1546, 1594, 1622, 1654, 1706, 1766, 1906, 1934

Offset: 1

Author

Zak Seidov, Jun 08 2006

Keywords

• nonn

Comments

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).

Crossrefs

Cf. A119616.

Programs

Mathematica

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]]