A052020 Sum of digits of k is a prime proper factor of k.

12, 20, 21, 30, 50, 70, 102, 110, 111, 120, 133, 140, 200, 201, 209, 210, 230, 247, 300, 308, 320, 322, 364, 407, 410, 476, 481, 500, 506, 511, 605, 629, 700, 704, 715, 782, 803, 832, 874, 902, 935, 1002, 1010, 1011, 1015, 1020, 1040, 1066, 1088, 1100, 1101

Offset: 1

Author

Patrick De Geest, Nov 15 1999

Keywords

• nonn
• base
• easy

Comments

For each prime p there are infinitely many terms with sum of digits p. - Robert Israel, Feb 26 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052018, A052019, A052021, A052022, A007953, A005349, A028834.

Programs

Maple

filter:= proc(n) local s;
  s:= convert(convert(n,base,10),`+`);
  isprime(s) and (n mod s = 0)
end proc:
select(filter, [$10..10^4]); # Robert Israel, Feb 26 2017

Mathematica

Select[Range[0, 2000], With[{s = DigitSum[#]}, s < # && Divisible[#, s] && PrimeQ[s]] &] (* Paolo Xausa, May 18 2024 *)

Python

from sympy import isprime
def ok(n):
    sd = sum(map(int, str(n)))
    return 1 < sd < n and n%sd == 0 and isprime(sd)
print([k for k in range(1102) if ok(k)]) # Michael S. Branicky, Dec 20 2021