A056777 Composite numbers k such that both phi(k+12) = phi(k) + 12 and sigma(k+12) = sigma(k) + 12.

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

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 congruent to 65 (mod 72). - Ralf Stephan, Jul 07 2003

Links

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

Example

k = 209 = 11*19, k + 12 = 221 = 13*17, phi(k + 12) = 192 = 180 + 12 = phi(k) + 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