A333079 - OEIS

%I #26 Jan 16 2024 13:52:14

%S 345,1645,6489,8041,23881,88473,115957,342637,3256261,4114285,4646101,

%T 5054221,13384681,17897737,20901553,23807821,42081409,64580041,

%U 65380921,70366153,82175857,110344621,137331565,164109901,286078081,331957897,366611617,367891717,489645157

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

%C A divisor of n other than 1 and n is called a nontrivial divisor of n.

%C 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

%C Each term in this sequence has at least eight divisors. - _Bernard Schott_, Mar 09 2020

%e 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.

%t Select[Range[10^5], 2 # / FactorInteger[#][[1, 1]] == DivisorSigma[1, #] - # - 1 &] (* _Giovanni Resta_, Mar 07 2020 *)

%t 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 *)

%o (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

%Y Cf. A032742.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Mar 07 2020

%E More terms from _Giovanni Resta_, Mar 07 2020