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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Harvey P. Dale)

Example

1122 = 2*3*11*17 and 1122 is divisible by 2+3+11+17 = 33.

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

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 *)

Prog

(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

Crossrefs

Sequence union A000040 = A005117 intersect A086486. - Ray Chandler, Nov 29 2011

Sequence in context: A325378 A164596 A295102 * A301900 A357854 A071141

Adjacent sequences: A131644 A131645 A131646 * A131648 A131649 A131650

Keyword

nonn

Author

Tanya Khovanova, Sep 08 2007

Status

approved