A074393 Number of primes between sigma(n) and phi(n) exclusive, minus 1 if sigma(n) is a prime

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

Antti Karttunen, Table of n, a(n) for n = 1..20000

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}]

Prog

(PARI) A074393(n) = if(n<=2, 0, my(s=sigma(n)); ((primepi(s-1)-primepi(eulerphi(n)))-isprime(s))); \\ Antti Karttunen, Jan 21 2025

Crossrefs

Sequence in context: A318281 A126114 A323458 * A267633 A095666 A257231

Adjacent sequences: A074390 A074391 A074392 * A074394 A074395 A074396

Keyword

nonn,changed

Author

Joseph L. Pe, Sep 24 2002

Extensions

Name modified to match terms by Sean A. Irvine, Jan 20 2025

Status

approved