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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 02:41 EDT 2021. Contains 343937 sequences. (Running on oeis4.)