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A230110 Composite numbers n such that 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). 2
8, 10, 30, 63, 64, 512, 588, 720, 800, 1320, 3960, 4096, 5184, 5760, 6400, 7200, 21600, 27720, 27900, 32768, 35280, 41472, 46080, 51200, 70840, 84672, 92400, 95040, 105600, 151200, 188160, 262144, 331776, 368640, 376320, 409600, 504000, 518400, 576000, 640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

Prime factors of 3960 are 2^3, 3^2, 5 and 11.

sum_{i=1..7} (p(i)/(p(i)+1))=3*[2/(2+1)]+2*[3/(3+1)]+5/(5+1)+11/(11+1)=21/4.

product_{i=1..7} (p(i)/(p(i)-1))=[2/(2+1)]^3*[3/(3-1)]^2*5/(5-1)*11/(11-1)=99/4.

Their sum is integer: 21/4 + 99/4 = 30.

MAPLE

with(numtheory); P:=proc(i) local b, 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: P(10^7);

CROSSREFS

Cf. A199767, A198391, A227034, A227248, A230111, A230112.

Sequence in context: A007939 A212767 A126807 * A223587 A245199 A242506

Adjacent sequences:  A230107 A230108 A230109 * A230111 A230112 A230113

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 09 2013

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.