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URL: https://oeis.org/A333079

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A333079
The largest nontrivial divisor of n equals the sum of the other nontrivial divisors of n.
0
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
OFFSET
1,1
COMMENTS
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
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A032742.
Sequence in context: A063370 A095963 A247079 * A236731 A138043 A048904
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Mar 07 2020
EXTENSIONS
More terms from Giovanni Resta, Mar 07 2020
STATUS
approved