A230111 Composite numbers m 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 m (with multiplicity).

8, 10, 64, 512, 720, 800, 1320, 1944, 4096, 5184, 5760, 6400, 7200, 8370, 23520, 32768, 41472, 44000, 46080, 47040, 51200, 69580, 74088, 76096, 84672, 93000, 95040, 105600, 129360, 235200, 240000, 262144, 331776, 368640, 409600, 518400, 546480, 576000, 640000

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Example

Prime factors of 7200 are 2^5, 3^2 and 5^2.
Sum_{i=1..9} (p(i)/(p(i)+1)) = 5*(2/(2+1)) + 2*(3/(3+1)) + 2*(5/(5+1)) = 13/2.
Product_{i=1..9} (p(i)/(p(i)-1)) = (2/(2+1))^5 * (3/(3-1))^2 * (5/(5-1))^2 = 225/2.
Their sum is an integer: 13/2 - 225/2 = -106.

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, A230110, A230112.

Sequence in context: A167303 A025634 A038288 * A289664 A321881 A204324

Adjacent sequences: A230108 A230109 A230110 * A230112 A230113 A230114

Keyword

nonn

Author

Paolo P. Lava, Oct 09 2013

Status

approved