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Search: id:A119623
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| A119623 |
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Composite numbers for which the second elementary symmetric function of divisors (s2) is prime. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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MATHEMATICA
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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]]
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CROSSREFS
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Cf. A119616.
Sequence in context: A055163 A119431 A023387 this_sequence A129119 A074980 A059218
Adjacent sequences: A119620 A119621 A119622 this_sequence A119624 A119625 A119626
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov, Jun 08 2006
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