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A212921
Composite number n = Product(p_j^k_j) that under the iteration of the map Product (p_j^k_j) -> Sum (p_j * k_j) reaches a limit that divides the number itself.
1
4, 15, 20, 21, 35, 42, 55, 65, 70, 95, 100, 105, 110, 120, 125, 130, 135, 140, 150, 160, 161, 170, 180, 182, 187, 190, 200, 203, 217, 220, 225, 231, 240, 260, 270, 280, 285, 301, 305, 312, 315, 319, 322, 340, 343, 351, 365, 370, 371, 375, 395, 400, 406, 407
OFFSET
1,1
COMMENTS
Apart from the case n=4, the limit of the iteration is a prime number.
LINKS
EXAMPLE
70 = 2*5*7 -> 2+5+7 = 14 =2*7 -> 2+7=9 = 3^2 -> 3*2=6=2*3 -> 2+3=5 and 70/5=14.
MAPLE
with(numtheory);
A212921:=proc(q)
local a, b, c, d, i, k, n;
print(4);
for n from 5 to q do
if not isprime(n) then a:=n;
while not isprime(a) do
b:=ifactors(a)[2]; c:=nops(b); b:=op(b); d:=0;
if c=1 then d:=b[1]*b[2];
else for k from 1 to c do d:=d+b[k][1]*b[k][2]; od; fi;
a:=d; if isprime(d) then if trunc(n/d)=n/d then lprint(n, d); fi; break; fi; od;
fi;
od;
end:
A212921(10000);
MATHEMATICA
it[n_] := it[n] = Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; Dot[p, e]]; it2[n_] := FixedPointList[it[#] &, n]; Select[Range[2, 1000], ! PrimeQ[#] && Mod[#, it2[#][[-1]]] == 0 &] (* T. D. Noe, Jun 01 2012 *)
CROSSREFS
Cf. A029909.
Sequence in context: A190709 A166732 A022133 * A359958 A225562 A301707
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 31 2012
STATUS
approved