A117843 Primes produced by a pyramidal ( three variable sequence) that is based on the Euler totient and multiperfect sigma functions.

2, 3, 5, 7, 11, 13, 17, 19, 29, 43, 173, 179, 193, 683, 1657, 2731, 3677, 3733, 4001, 5743, 7823, 7841, 7901, 9421, 63031, 63773, 93287, 157229, 213539, 235447, 1008503, 1849259, 3144571, 16262297, 4146957827, 24968880823, 499377616471

Offset

1,1

Comments

This function is Gaukman type of prime function in three variables.

Links

Table of n, a(n) for n=1..37.

Formula

phi[p_] = p*(p + gap) - p - (p + gap) + 1 sigma[p_] = gap*p*(p + gap) r0,r1 solutions to: phi[n+2]=sigma[n] f[n0_, m_, gap_] = ((r0)^n0 + (r1)^n0)/gap^m a(n) = if[PrimeQ[f[n,m,2*k]]==True.f[n,m,2*k]]

Mathematica

phi[p_] = p*(p + gap) - p - (p + gap) + 1 a = phi[n + 2] sigma[p_] = gap*p*(p + gap) b = sigma[n] c = Expand[a - b] a = Table[Table[Table[Floor[f[n, m, 2*k]], {m, 1, n}], {n, 1, 10}], {k, 1, 10}] aa = Flatten[a] pp = Union[Abs[Flatten[Table[ If[PrimeQ[aa[[n]]], aa[[n]], {}], {n, 1, Length[aa]}]]]]

Crossrefs

Cf. A001359.

Sequence in context: A124589 A079150 A177000 * A293667 A068192 A225083

Adjacent sequences: A117840 A117841 A117842 * A117844 A117845 A117846

Keyword

nonn,uned

Author

Roger L. Bagula, Apr 30 2006

Status

approved