A144970 Integers in the sequence of rationals defined by b(1) = 61, b(n) = b(n-1) + (n+60)/n for n > 1.

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.

Links

Table of n, a(n) for n=1..6.

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

Adjacent sequences: A144967 A144968 A144969 * A144971 A144972 A144973

Keyword

nonn,fini,full,less

Author

Vladimir Joseph Stephan Orlovsky, Sep

Extensions

Edited definition. Added comment, example, PARI code, cross-reference and keywords. Changed offset. - Klaus Brockhaus, Oct 16 2008

Status

approved