A074397 Number of primes between sigma(n) and n.

0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 0, 4, 0, 3, 3, 4, 0, 5, 0, 5, 3, 3, 0, 8, 1, 4, 3, 7, 0, 10, 0, 7, 4, 5, 4, 13, 0, 5, 4, 12, 0, 11, 0, 9, 7, 6, 0, 15, 1, 9, 5, 10, 0, 14, 4, 14, 6, 8, 0, 22, 0, 6, 9, 12, 5, 16, 0, 11, 5, 15, 0, 24, 0, 9, 9, 13, 3, 18, 0, 20, 8, 8, 0, 25, 5, 9, 7, 18, 0, 27, 5, 15, 7

Offset

1,6

Links

Table of n, a(n) for n=1..93.

Example

sigma(6) = 12 and there are 2 primes between 6 and 12 (endpoints are excluded), namely 7, 11. Hence a(6) = 2.

Mathematica

(*gives number of primes < n*) f[n_] := Module[{r, i}, r = 0; i = 1; While[Prime[i] < n, i++ ]; i - 1]; (*gives number of primes between m and n with endpoints excluded*) g[m_, n_] := Module[{r}, r = f[m] - f[n]; If[PrimeQ[n], r = r - 1]; r]; Table[g[DivisorSigma[1, n], n], {n, 1, 100}]

Crossrefs

Sequence in context: A138036 A354856 A055136 * A345039 A082023 A349438

Adjacent sequences: A074394 A074395 A074396 * A074398 A074399 A074400

Keyword

nonn

Author

Joseph L. Pe, Sep 24 2002

Status

approved