A243226 - OEIS

A243226

Let s(m) = Sum_{j=1..m} sigma(j)/j where sigma(j) is the sum of divisors of j. Sequence consists of numbers k such that denominator(s(k)) < denominator(s(k-1)).

10, 50, 55, 69, 77, 102, 184, 185, 186, 238, 250, 261, 268, 322, 483, 522, 605, 620, 671, 693, 774, 847, 1159, 1204, 1222, 1250, 1316, 1507, 1548, 1587, 1734, 1870, 1880, 1938, 2032, 2055, 2212, 2409, 2440, 2575, 2653, 3082, 3399, 3416, 3448, 3685, 4033, 4046

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Overall the sequence defined by s(m) = Sum_{j=1..m} sigma(j)/j has increasing denominators, but there are some values of m where the denominators locally decrease.

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

EXAMPLE

The first 10 terms of {s(n)} are 1, 5/2, 23/6, 67/12, 407/60, 527/60, 4169/420, 9913/840, 33379/2520, 7583/504.

Since denominator(s(10)) < denominator(s(9)), 10 is in the sequence.

MAPLE

N:= 10^4: # to get all terms <= N

tot:= 0:

for n from 1 to N+1 do tot:= tot+numtheory:-sigma(n)/n; sd[n]:= denom(tot) od:

select(t -> sd[t] < sd[t-1], [$2..N]); # Robert Israel, Aug 22 2014

PROG

(PARI) lista(nn) = {s = 1; lastd = 1; for (n=2, nn, s += sigma(n)/n; newd = denominator(s); if (newd < lastd, print1(n, ", "); ); lastd = newd; ); }