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A131647 Composite numbers that are products of distinct primes and divisible by the sum of those primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A131647 union A000040 = A005117 intersect A086486. - Ray Chandler, Nov 29 2011

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..2000

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 in context: A112343 A182996 A164596 * A071141 A071312 A071142

Adjacent sequences:  A131644 A131645 A131646 * A131648 A131649 A131650

KEYWORD

nonn

AUTHOR

Tanya Khovanova, Sep 08 2007

STATUS

approved

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Last modified August 24 02:32 EDT 2017. Contains 291052 sequences.