OFFSET
1,2
COMMENTS
Sometimes referred to as balanced numbers.
The sequence is infinite because for k>= 1, phi(10^k) = 4*10^(k-1) and digitsum (10^k) = 1. - Marius A. Burtea, Dec 20 2018
If n is in the sequence, then so is 10*n. - Robert Israel, Dec 20 2018
REFERENCES
James J. Tattersall, Elementary Number Theory in Nine Chapters, 2nd ed., Cambridge University Press, 2005, page 193, exercise 15.
LINKS
Marius A. Burtea and Muniru A Asiru, Table of n, a(n) for n = 1..10000 (first 3028 terms from Marius A. Burtea)
EXAMPLE
39 is in the sequence since its sum of digits (12) divides phi(39) = 24.
MAPLE
select(n -> numtheory:-phi(n) mod convert(convert(n, base, 10), `+`) = 0, [$1..1000]); # Robert Israel, Dec 20 2018
MATHEMATICA
Select[Range[1000], Mod[EulerPhi[#], Total @ IntegerDigits[#]] == 0 &] (* Giovanni Resta, Mar 16 2013 *)
PROG
(Magma) [n: n in [1..1000] | IsIntegral((EulerPhi(n))/&+Intseq(n))]; // Marius A. Burtea, Dec 20 2018
(GAP) nmax:=150;;
S:=List(List([1..nmax], n->ListOfDigits(n)), Sum);; P:=List([1..nmax], n->Phi(n));;
a:=Filtered([1..nmax], i->P[i] mod S[i]=0); # Muniru A Asiru, Dec 20 2018
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Jayanta Basu, Mar 16 2013
STATUS
approved