A224912 Numbers m for which Sum_{i=1..k} (p(i)/(p(i)-1)) + Product_{i=1..k} (p(i)/(p(i)-1)) is an integer, where p(i) are the k prime factors of m (with multiplicity).

2, 3, 4, 8, 16, 32, 36, 64, 72, 108, 128, 144, 200, 256, 288, 396, 512, 528, 576, 588, 1024, 1040, 1152, 1296, 2000, 2048, 2304, 2320, 2400, 2592, 3888, 4096, 4160, 4608, 4752, 4800, 5184, 5600, 6552, 7200, 8192, 8448, 9216, 9600, 9936, 10368, 11316, 12000

Offset

1,1

Comments

Apart from 3 all terms are even.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Example

Prime factors of 11316 are 2^2, 3, 23 and 41.
Sum_{i=1..5} (p(i)/(p(i)-1)) = 2*(2/(2-1)) + 3/(3-1) + 23/(23-1) + 41/(41-1) = 3331/440.
Sroduct_{i=1..5} (p(i)/(p(i)-1)) = 2*(2/(2-1)) * 3/(3-1) * 23/(23-1) * 41/(41-1) = 2829/440.
Their sum is an integer: 3331/440 + 2829/440 = 14.

Maple

with(numtheory);
A224912:=proc(i) local b, c, d, n, p;
for n from 2 to i do p:=ifactors(n)[2];
  b:=add(op(2, d)*op(1, d)/(op(1, d)-1), d=p)+mul((op(1, d)/(op(1, d)-1))^op(2, d), d=p);
  if trunc(b)=b then print(n); fi; od; end:
A224912(10^6);

Crossrefs

Cf. A199767, A198391.

Sequence in context: A118841 A126294 A339973 * A162724 A244750 A140974

Adjacent sequences: A224909 A224910 A224911 * A224913 A224914 A224915

Keyword

nonn

Author

Paolo P. Lava, Apr 19 2013

Status

approved