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A074393
Number of primes between sigma(n) and phi(n).
0
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.
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
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Sep 24 2002
STATUS
approved