

A117843


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


0



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
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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



