A003635 Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10).

62, 63, 65, 75, 84, 95, 161, 173, 195, 216, 261, 266, 272, 276, 326, 371, 372, 377, 381, 383, 386, 387, 395, 411, 416, 422, 426, 431, 432, 438, 441, 443, 461, 466, 471, 476, 482, 483, 486, 488, 491, 492, 493, 494, 497, 498, 516, 521, 522, 527, 531, 533, 536

Offset: 1

Author

N. J. A. Sloane and Mira Bernstein

Keywords

• nonn
• easy
• nice
• base

References

• J. H. Conway, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10867
• Giovanni Resta, Numbers Aplenty: Inconsummate numbers

Crossrefs

Cf. A003634, A052489, A052490, A052491, A058898-A058917.

Programs

Maple

For Maple code see A058906.

Mathematica

nmax = 1000; Reap[ Do[k = n; kmax = 100*n; While[ Tr[ IntegerDigits[k]]*n != k && k < kmax, k = k + n]; If[k == kmax, Sow[n]], {n, 1, nmax}]][[2, 1]] (* Jean-François Alcover, Jul 12 2012 *)

Python

from itertools import count, islice, combinations_with_replacement
def A003635_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 9*l*n < 10**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(10),l):
                if (s:=sum(d))>0 and sorted(str(s*n)) == [str(e) for e in d]:
                    break
            else:
                continue
            break
A003635_list = list(islice(A003635_gen(),20)) # Chai Wah Wu, May 09 2023