A003635 - OEIS

A003635

Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10).
(Formerly M5325)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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 *)

PROG

(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