A165209 Numbers whose digital sum is divisible by the digital sum of its divisors.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 81, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173

Offset

1,2

Comments

All primes are terms of this sequence.

Nonprime terms begin 1, 4, 6, 8, 9, 22, 26, 27, ...

This sequence deviates from A072227; they first differ at n=40: a(40) = 81 while A072227(40) = 82. Each of the first 65 terms of A072227 is a term of this sequence. Sequence of different terms: 81, ..., ?

A072227 is not a subsequence; A072227(256) = 1089 and 363 divides 1089 but 3+6+3 does not divide 1+0+8+9. - Charles R Greathouse IV, Sep 12 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(40) = 81, the divisors of 81 are 1, 3, 9, 27, 81, with digital sums 1, 3, 9, 9, 9 which all divide the digital sum of 81, i.e., 9.

Mathematica

dsdQ[n_]:=Module[{dsn=Total[IntegerDigits[n]], dsd=Total[ IntegerDigits[ #]]&/@ Divisors[n]}, And@@Divisible[dsn, dsd]]; Select[Range[200], dsdQ] (* Harvey P. Dale, Aug 11 2014 *)

Prog

(PARI) dsum(n)=my(s); while(n, s+=n%10; n\=10); s
is(n)=my(t=dsum(n)); fordiv(n, d, if(t%dsum(d), return(0))); 1 \\ Charles R Greathouse IV, Sep 12 2012
(Python)
from sympy import divisors
def ds(n): return sum(map(int, str(n)))
def ok(n):
    dsn = ds(n)
    return all(dsn%ds(d) == 0 for d in divisors(n, generator=True))
print([k for k in range(1, 174) if ok(k)]) # Michael S. Branicky, Jun 25 2022

Crossrefs

Cf. A072227.

Sequence in context: A225657 A175772 A124868 * A072227 A122427 A161597

Adjacent sequences: A165206 A165207 A165208 * A165210 A165211 A165212

Keyword

nonn,base

Author

Jaroslav Krizek, Sep 07 2009

Status

approved