A074393 Number of primes between sigma(n) and phi(n).

0, 0, 1, 1, 1, 4, 1, 4, 1, 5, 1, 7, 1, 6, 5, 5, 1, 9, 1, 9, 6, 7, 1, 13, 1, 8, 5, 11, 1, 16, 1, 12, 7, 10, 6, 19, 1, 10, 7, 18, 1, 19, 1, 15, 12, 12, 1, 24, 3, 16, 9, 16, 1, 23, 8, 21, 11, 15, 1, 33, 1, 14, 16, 18, 8, 26, 1, 19, 10, 25, 1, 35, 1, 19, 18, 23, 7, 30, 1, 31, 14, 18, 1, 39, 10, 19

Offset

1,6

Comments

a(n) appears to be nonzero for n > 2.

Links

Table of n, a(n) for n=1..86.

Example

sigma(6) = 12 and phi(6) = 2. There are 4 primes between 12 and 2 (endpoints are excluded), namely 3, 5, 7, 11. Hence a(6) = 4.

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[m], r = r - 1]; If[PrimeQ[n], r = r - 1]; r]; Table[g[DivisorSigma[1, n], EulerPhi[n]], {n, 1, 100}]

Crossrefs

Sequence in context: A318281 A126114 A323458 * A267633 A095666 A257231

Adjacent sequences: A074390 A074391 A074392 * A074394 A074395 A074396

Keyword

nonn

Author

Joseph L. Pe, Sep 24 2002

Status

approved