This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(3) = 3. A086487(3) = 30 /(2+3+5) = 3.
30 is a member. The prime divisors of 30 are 2, 3 and 5 and 2+3+5 = 10, divides 30. 84, however, is not a member because the sum of its distinct prime divisors (2+3+7=12) does not divide the product of its distinct prime divisors (2*3*7=42), even though 12 does divide 84. - _Harvey P. Dale_, Nov 26 2011, based on a comment from _Ray Chandler_
sdpQ[n_]:=Module[{dpds=Transpose[FactorInteger[n]][[1]]}, Divisible[ Times@@dpds,Total[dpds]]]; Select[Range[2,200],sdpQ] (* Harvey P. Dale, Nov 26 2011 *)
a(5) = 72 = 2*2*2*3*3; 2+2+2+3+3 = 12 divides 72.
a(4) = 840 = 2^3*3*5*7; 2+2+2+3+5+7 = 21 divides 840.
a(5) = 15015 = 3*5*7*11*13 is the product of 5 consecutive primes and is divisible by 3+5+7+11+13 = 39.
f:= proc(n) local L,i,p;
L:= [seq(ithprime(i),i=1..n)]:
p:= convert(L,`*`);
if n::even then
if p mod convert(L,`+`) = 0 then return p else return 0 fi
else
do
p:= convert(L,`*`);
if p mod convert(L,`+`) = 0 then return p fi;
if p > 10^225 then return FAIL fi;
L:= [op(L[2..-1]),nextprime(L[-1])];
od
fi;
end proc:
map(f, [$1..26]);
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