A203461 Let a(n) and the ratio r(n) = greatest prime divisor of a(n) / sum of the distinct prime divisors of a(n). The sequence a(n) is defined by the recurrence a(1) = 2, a(n+1) such that r(n+1) < r(n).

2, 6, 30, 105, 210, 2002, 2310, 3003, 5005, 10010, 15015, 30030, 46189, 92378, 138567, 230945, 323323, 646646, 969969, 1616615, 3233230, 4849845, 9699690, 37182145, 74364290, 111546435, 223092870, 3234846615, 6469693230

Offset

1,1

Comments

See the same problem with the sequence A002182 where the ratio r(n) = a(n) / sigma(a(n)).

Links

Table of n, a(n) for n=1..29.

Example

a(3) = 30 because the ratio r(3) = 5 /(2+3+5) = 0.5 is smaller than r(2) = 3/(2 + 3) = 0.6

Maple

with(numtheory):r0:=10^10:for x from 2 to 10^7 do: y:=factorset(x):n1:=nops(y):s:=sum(y[i], i=1..n1):r:= evalf(y[n1]/s):if r < r0 then r0:=r: print(x):else fi:od:

Crossrefs

Cf. A008472, A002182.

Sequence in context: A051844 A335396 A034501 * A071758 A071760 A304579

Adjacent sequences: A203458 A203459 A203460 * A203462 A203463 A203464

Keyword

nonn

Author

Michel Lagneau, Jan 02 2012

Status

approved