A247140 Number of distinct values obtained from 1 to n when listing all distinct values of both numerators and denominators of sigma(n)/n.

1, 3, 4, 5, 7, 7, 8, 9, 11, 11, 13, 13, 14, 14, 14, 16, 18, 18, 20, 22, 23, 23, 25, 25, 26, 26, 28, 28, 30, 30, 30, 31, 31, 31, 33, 35, 37, 37, 39, 39, 41, 41, 43, 43, 44, 44, 45, 45, 47, 49, 49, 49, 51, 51, 53, 53, 54, 55, 57, 57, 59, 59, 60, 62, 64, 64, 66

Offset

1,2

Comments

For n=100, a(n)/n = 0.93; for n=1000, a(n)/n = 0.799; for n=10000, a(n)/n = 0.7326.

Links

Table of n, a(n) for n=1..67.

Example

For n=1, sigma(n)/n = 1/1, so the set of distinct values so far is {1}, and the number of terms of this set is 1.
For n=2, sigma(n)/n = 3/2, so the set of distinct values so far is {1, 2, 3}, and the number of terms of this set is 3.
For n=3, sigma(n)/n = 4/3, so the set of distinct values so far is {1, 2, 3, 4}, and the number of terms of this set is 4.

Prog

(PARI) nbnd(n, vtot) = {ab = sigma(n)/n; if (! vecsearch(vtot, num=numerator(ab)), vtot = vecsort(concat(vtot, num))); if (! vecsearch(vtot, den=denominator(ab)), vtot = vecsort(concat(vtot, den))); return (vtot); }
lista(nn) = {vtot = []; for (n=1, nn, vtot = nbnd(n, vtot); print1(#vtot, ", "); ); }

Crossrefs

Cf. A000203 (sigma(n)), A017665 (numerator of sigma(n)/n), A017666 (denominator).

Sequence in context: A389466 A049465 A196122 * A269304 A071054 A379337

Adjacent sequences: A247137 A247138 A247139 * A247141 A247142 A247143

Keyword

nonn

Author

Michel Marcus, Nov 20 2014

Status

approved