A131647 Composite numbers that are products of distinct primes and divisible by the sum of those primes.
30, 70, 105, 231, 286, 627, 646, 805, 897, 1122, 1581, 1798, 2730, 2958, 2967, 3055, 3526, 3570, 4070, 4543, 5487, 5658, 6461, 6745, 7198, 7881, 8778, 8970, 9222, 9282, 9717, 10366, 10370, 10626, 10707, 11130, 14231, 15015, 16377, 16530, 19866
Offset: 1
Keywords
Examples
1122 = 2*3*11*17 and 1122 is divisible by 2+3+11+17 = 33.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Harvey P. Dale)
Crossrefs
Programs
-
Maple
with(numtheory): P:=proc(q) local a,k,n; for n from 2 to q do if issqrfree(n) and not isprime(n) then a:=ifactors(n)[2]; if type(n/add(a[k][1],k=1..nops(a)),integer) then print(n); fi; fi; od; end: P(10^9); # Paolo P. Lava, Sep 19 2014
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Mathematica
Select[Range[2, 20000], PrimeQ[ # ] == False && Union[Transpose[FactorInteger[ # ]][[2]]] == {1} && Mod[ #, Plus @@ Transpose[FactorInteger[ # ]][[1]]] == 0 &] pdpQ[n_]:=Module[{fi=Transpose[FactorInteger[n]]},!PrimeQ[n]&&Max[fi[[2]]] == 1&&Divisible[n,Total[fi[[1]]]]]; Select[Range[2,50000],pdpQ] (* Harvey P. Dale, Oct 16 2013 *) -
PARI
lista(nn) = {forcomposite(n=1, nn, f = factor(n); nbp = #f~; if ((vecmax(f[,2]) == 1) && !(n % sum(i=1, nbp, f[i, 1])), print1(n, ", ")););} \\ Michel Marcus, Sep 19 2014