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A144970
Integers in the sequence of rationals defined by b(1) = 61, b(n) = b(n-1) + (n+60)/n for n > 1.
0
61, 92, 113, 129, 142, 153
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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.
MATHEMATICA
lst={}; q=60; s=0; Do[s+=n/(n-q); If[s==IntegerPart[s], AppendTo[lst, s]], {n, q+1, q+4!}]; lst
Select[RecurrenceTable[{a[1]==61, a[n]==a[n-1]+(n+60)/n}, a, {n, 20}], IntegerQ] (* Harvey P. Dale, Feb 28 2015 *)
PROG
(PARI) {s=0; for(n=1, 10, s=s+(n+60)/n; if(denominator(s)==1, print1(s, ", ")))}
CROSSREFS
Cf. A033380 ([ 60/n ]).
Sequence in context: A123207 A309180 A038856 * A045562 A104229 A088787
KEYWORD
nonn,fini,full,less
EXTENSIONS
Edited definition. Added comment, example, PARI code, cross-reference and keywords. Changed offset. - Klaus Brockhaus, Oct 16 2008
STATUS
approved