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 A216836 Numbers n such that sum of decimal digits of n divides phi(n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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, 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

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Last modified August 4 08:30 EDT 2021. Contains 346445 sequences. (Running on oeis4.)