

A056777


Composite n such that both Phi(n+12)=Phi(n)+12 and Sigma(n+12)=Sigma(n)+12.


0



65, 209, 11009, 38009, 680609, 2205209, 3515609, 4347209, 10595009, 12006209, 31979009, 89019209, 169130009, 244766009, 247590209, 258084209, 325622009, 357777209, 377330609, 441630209, 496175609, 640343009, 1006475609
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OFFSET

1,1


COMMENTS

It is easy to show that if p, p+2, p+6 and p+8 are all prime (a prime quadruple as defined in A007530, which lists the values of p) with x=p(p+8), x+12=(p+2)(p+6), then x is in the sequence. I conjecture that all members of the sequence are of this form.  Jud McCranie, Oct 11 2000
Numbers so far are all 65 mod 72.  Ralf Stephan, Jul 07 2003


LINKS

Table of n, a(n) for n=1..23.


EXAMPLE

n = 209 = 11.19, n+12 = 221 = 13.17, Phi(n+12) = 192 = 180+12 = Phi(n)+12, also Sigma(221) = 252 = Sigma(209)+12 = 240+12.
phi(65)+12 = 60 = phi(65+12), sigma(65)+12 = 96 = sigma(65+12), 65 is composite.


PROG

(PARI) isok(n) = !isprime(n) && (sigma(n+12) == sigma(n)+12) && (eulerphi(n+12)==eulerphi(n)+12); \\ Michel Marcus, Jul 14 2017


CROSSREFS

Cf. A000010, A001838, A015917, A054902, A046133.
Sequence in context: A242318 A200867 A175795 * A048512 A237039 A305157
Adjacent sequences: A056774 A056775 A056776 * A056778 A056779 A056780


KEYWORD

nonn


AUTHOR

Labos Elemer, Aug 17 2000


EXTENSIONS

More terms from Jud McCranie, Oct 11 2000


STATUS

approved



