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A070814 Solutions to phi(gpf(x)) - gpf(phi(x)) = 14 = c are special multiples of 17, x = 17k, where greatest prime factors of factor k were observed from {2, 3, 5}, i.e., it is smaller than 17. See solutions to other even cases of c (=A070813): A007283 for 0, A070004 for 2, A070815 for 254, A070816 for 65534. Gpf = greatest prime factor. 2
17, 34, 51, 68, 85, 102, 136, 170, 204, 255, 272, 340, 408, 510, 544, 680, 816, 1020, 1088, 1360, 1632, 2040, 2176, 2720, 3264, 4080, 4352, 5440, 6528, 8160, 8704, 10880, 13056, 16320, 17408, 21760, 26112, 32640, 34816, 43520, 52224, 65280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n > 10, a(n) = 2a(n-4). First, it is easy to show that with i >= 0 and k,m in {0,1}, a(n) are of the form 2^i*3^k*5^m. Factoring this sequence reveals the regular pattern 2^i, 2^(i-2)*5, 2^(i-1)*3, 2^(i-3)*3*5, 2^(i+1), ... which obviously has the property a(n) = 2a(n-4) for n > 10. - Lambert Herrgesell (lambert.herrgesell(AT)googlemail.com), Jan 09 2007

LINKS

Table of n, a(n) for n=1..42.

FORMULA

For n > 10, a(n) = 2a(n-4) (conjectured). - Ralf Stephan, May 09 2004

EXAMPLE

For n = 32640 = 128*3*5*17, gpf(n) = 17, phi(n) = 16384, commutator[32640] = phi(17) - gpf(16384) = 16 - 2 = 14.

MATHEMATICA

pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 14], Print[{n, n/17, pf[n/17]}]], {n, 3, 1000000}] (* Terms of sequence are n *)

CROSSREFS

Cf. A000010, A000215, A006530, A007283, A070002, A070003, A070004, A070777, A070812, A070813.

Sequence in context: A033029 A044842 A033014 * A188290 A268287 A249988

Adjacent sequences:  A070811 A070812 A070813 * A070815 A070816 A070817

KEYWORD

nonn

AUTHOR

Labos Elemer, May 09 2002

STATUS

approved

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Last modified March 25 20:10 EDT 2019. Contains 321477 sequences. (Running on oeis4.)