A216836 Numbers n such that sum of decimal digits of n divides phi(n).

1, 10, 11, 13, 17, 20, 21, 27, 35, 39, 40, 41, 42, 43, 50, 54, 55, 57, 63, 80, 81, 82, 84, 86, 92, 93, 97, 100, 101, 105, 108, 110, 111, 112, 114, 116, 117, 122, 126, 129, 130, 131, 135, 142, 143, 147

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

Sequence in context: A121296 A121265 A045986 * A188165 A125588 A253205

Adjacent sequences: A216833 A216834 A216835 * A216837 A216838 A216839

Keyword

nonn,base,easy

Author

Jayanta Basu, Mar 16 2013

Status

approved