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A230112 Composite numbers n such that product_{i=1..k} (p_i/(p_i-1)) / sum_{i=1..k} (p_i/(p_i+1)) is an integer, where p_i are the k prime factors of n (with multiplicity). 2
4, 8, 16, 64, 256, 720, 800, 2200, 4096, 25600, 33600, 36288, 41472, 46080, 65536, 92400, 104960, 235200, 282240, 338688, 376320, 403200, 419840, 535680, 556640, 576000, 580800, 640000, 844800, 979776, 1088640, 1244160, 1354752, 1382400, 1505280, 1689600, 1995840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

Prime factors of 2200 are 2^3, 5^2 and 11.

sum_{i=1..6} (p(i)/(p(i)+1))=3*[2/(2+1)]+2*[5/(5+1)]+11/(11+1)=55/12.

product_{i=1..6} (p(i)/(p(i)-1))=[2/(2-1)]^3*[5/(5-1)]^2*11/(11-1)=55/4.

The ratio is integer: (55/4) / (55/12) = 3.

MAPLE

with(numtheory); P:=proc(q) local a, d, n, p;

for n from 2 to q do if not isprime(n) then p:=ifactors(n)[2];

a:=mul((op(1, d)/(op(1, d)-1))^op(2, d), d=p)/add((op(1, d)/(op(1, d)+1))*op(2, d), d=p); if type(a, integer) then print(n); fi; fi;

od; end: P(10^7);

CROSSREFS

Cf. A199767, A198391, A227034, A227248, A230110, A230111.

Sequence in context: A077447 A102358 A038238 * A023376 A242966 A038110

Adjacent sequences:  A230109 A230110 A230111 * A230113 A230114 A230115

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 09 2013

STATUS

approved

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Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.