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

1,1

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

Links

Table of n, a(n) for n=1..29.

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

Adjacent sequences: A333076 A333077 A333078 * A333080 A333081 A333082

Keyword

nonn

Author

Joseph L. Pe, Mar 07 2020

Extensions

More terms from Giovanni Resta, Mar 07 2020

Status

approved