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 A230111 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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 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 A204324 A070276 Adjacent sequences:  A230108 A230109 A230110 * A230112 A230113 A230114 KEYWORD nonn AUTHOR Paolo P. Lava, Oct 09 2013 STATUS approved

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