%I #9 Feb 28 2015 10:56:38

%S 61,92,113,129,142,153

%N Integers in the sequence of rationals defined by b(1) = 61, b(n) = b(n-1) + (n+60)/n for n > 1.

%C b(n) = n + 60*sum_{k=1..n} 1/k. For n >= 7 the denominator of sum_{k=1..n} 1/k is a multiple of 7, but 7 is not a divisor of 60. Hence b(n) is not an integer for n >= 7.

%e b(1) through b(10) are 61, 92, 113, 129, 142, 153, 1138/7, 2395/14, 7507/42, 7801/42; only the first six of them are integers.

%t lst={};q=60;s=0;Do[s+=n/(n-q);If[s==IntegerPart[s],AppendTo[lst,s]],{n,q+1,q+4!}];lst

%t Select[RecurrenceTable[{a[1]==61,a[n]==a[n-1]+(n+60)/n},a,{n,20}], IntegerQ] (* _Harvey P. Dale_, Feb 28 2015 *)

%o (PARI) {s=0; for(n=1, 10, s=s+(n+60)/n; if(denominator(s)==1, print1(s, ",")))}

%Y Cf. A033380 ([ 60/n ]).

%K nonn,fini,full,less

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Sep

%E Edited definition. Added comment, example, PARI code, cross-reference and keywords. Changed offset. - _Klaus Brockhaus_, Oct 16 2008