OFFSET
1,1
COMMENTS
Terms of A007283(n) are part of the sequence for n > 1. If x = 3*2^n then we have phi(3*2^n) = phi(3)*phi(2^n) = 2*(2-1)*2^(n-1) = 2^n and phi(n/3)+phi(n/2) = phi(2^n)+phi(3*2^(n-1)) = 2^(n-1)+2*(2-1)*2^(n-2) = 2*2^(n-1) = 2^n.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
Prime factors of 1365 are 3, 5, 7, 13 and phi(1365/3) + phi(1365/5) + phi(1365/7) + phi(1365/13) = 288 + 144 + 96 + 48 = 576 = phi(1365).
MAPLE
with(numtheory): P:=proc(n) local k;
if phi(n)=add(phi(n/k), k=factorset(n)) then n; fi; end:
seq(P(i), i=1..48384);
MATHEMATICA
Select[Range[2, 1000], EulerPhi[#] == Total@EulerPhi[#/FactorInteger[#][[;; , 1]]] &] (* Amiram Eldar, Mar 20 2019 *)
PROG
(PARI) isok(n) = my(f=factor(n)[, 1]); eulerphi(n) == sum(k=1, #f, eulerphi(n/f[k])); \\ Michel Marcus, Mar 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 19 2019
STATUS
approved