A333079 The largest nontrivial divisor of n equals the sum of the other nontrivial divisors of n.

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

Author

Joseph L. Pe, Mar 07 2020

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A032742.

Programs

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 *)

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

Extensions

More terms from Giovanni Resta, Mar 07 2020