A063693 - OEIS

%I #9 Jun 25 2018 22:57:06

%S 3,5,11,17,24,29,41,42,56,59,71,98,101,102,107,137,149,179,191,197,

%T 227,230,239,248,264,269,281,294,311,347,419,431,461,468,521,569,599,

%U 617,638,641,659,809,821,827,857,881,1014,1016,1019,1031,1049,1061,1078

%N Numbers k such that phi(k + d(k)) = phi(k) + d(k), where phi() = A000010(), d() = A000005().

%H Harry J. Smith, <a href="/A063693/b063693.txt">Table of n, a(n) for n = 1..1000</a>

%e Primes and composites among solutions:

%e k = 59, d(58) = 2, phi(59) = 58, phi(59+2) = phi(61) = 60 = phi(59) + d(59);

%e k = 56, d(56) = 8, phi(56) = 24, phi(56+8) = phi(64) = 32 = phi(56) + d(56).

%o (PARI) { n=0; for (x=1, 10^9, if (eulerphi(x + numdiv(x)) == (eulerphi(x) + numdiv(x)), write("b063693.txt", n++, " ", x); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 27 2009

%Y Cf. A000005, A000010.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 23 2001