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A224912 Numbers n 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 n (with multiplicity). 4
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 (list; graph; refs; listen; history; text; internal format)
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.

product_{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 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: A189740 A118841 A126294 * A162724 A244750 A140974

Adjacent sequences:  A224909 A224910 A224911 * A224913 A224914 A224915

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Apr 19 2013

STATUS

approved

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Last modified February 27 06:03 EST 2020. Contains 332299 sequences. (Running on oeis4.)