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A291192
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Squarefree composite numbers n such that n*sigma(n) is of the form k*(k+1).
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1
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6, 42, 1430, 3686, 5685, 23815, 60235, 129778, 370991, 652289, 654545, 660265, 795405, 801645, 1532170, 3413267, 3457597, 4235270, 4282330, 8107937, 9679187, 10835013, 15464685, 15963578, 16636503, 24976497, 28122458, 29595310, 34759879, 35642479, 58525286
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OFFSET
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1,1
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COMMENTS
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Also squarefree composite numbers n such that Product_{p|n, p prime} A002378(p) is in A002378.
Is this sequence infinite?
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LINKS
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EXAMPLE
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42 = 2*3*7 is a term because 42*sigma(42) = 42(2+1)(3+1)(7+1) = 4032 = 63*64.
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MATHEMATICA
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Select[Range[586*10^5], CompositeQ[#]&&SquareFreeQ[#]&&OddQ[Sqrt[1+4(# DivisorSigma[ 1, #])]]&] (* Harvey P. Dale, Nov 23 2023 *)
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PROG
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(PARI) is(n, f=factor(n))=#f~>1 && vecmax(f[, 2])==1 && ispolygonal(n*sigma(f)/2, 3)
list(lim)=my(v=List()); forfactored(n=6, lim\1, if(call(is, n), listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Aug 22 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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