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

1,1

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).

Links

Table of n, a(n) for n=1..45.

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]]

Crossrefs

Cf. A119616.

Sequence in context: A315237 A315238 A315239 * A129119 A259020 A259021

Adjacent sequences: A119620 A119621 A119622 * A119624 A119625 A119626

Keyword

nonn

Author

Zak Seidov, Jun 08 2006

Status

approved