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A333079
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The largest nontrivial divisor of n equals the sum of the other nontrivial divisors of n.
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0
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345, 1645, 6489, 8041, 23881, 88473, 115957, 342637, 3256261, 4114285, 4646101, 5054221, 13384681, 17897737, 20901553, 23807821, 42081409, 64580041, 65380921, 70366153, 82175857, 110344621, 137331565, 164109901, 286078081, 331957897, 366611617, 367891717, 489645157
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OFFSET
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1,1
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COMMENTS
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A divisor of n other than 1 and n is called a nontrivial divisor of n.
In general, if p, p+k, and q = (p^2+(2+k)*p+k)/(k-1) are 3 primes and p < p+k < q, then p(p+k)q is a term. In particular, if p, p+2, and p^2+4*p+2 are 3 primes, then p(p+2)(p^2+4*p+2) is a term. - Giovanni Resta, Mar 08 2020
Each term in this sequence has at least eight divisors. - Bernard Schott, Mar 09 2020
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LINKS
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EXAMPLE
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The nontrivial divisors of 345 are 3, 5, 15, 23, 69, 115, the largest of which, 115, is equal to the sum of the other nontrivial divisors 3, 5, 15, 23, 69.
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MATHEMATICA
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Select[Range[10^5], 2 # / FactorInteger[#][[1, 1]] == DivisorSigma[1, #] - # - 1 &] (* Giovanni Resta, Mar 07 2020 *)
lndQ[n_]:=With[{c=TakeDrop[Rest[Most[Divisors[n]]], -1]}, c[[1, 1]]==Total[c[[2]]]]; Select[Range[ 51*10^5], lndQ]//Quiet (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jan 16 2024 *)
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PROG
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(PARI) for(k=2, 5*10^7, my(d=divisors(k)); if(#d>2&&d[#d-1]==vecsum(d[2..#d-2]), print1(k, ", "))) \\ Hugo Pfoertner, Mar 07 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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