A050220 Larger of Smith brothers.

729, 2965, 3865, 4960, 5936, 6188, 9387, 9634, 11696, 13765, 16537, 16592, 20785, 25429, 28809, 29624, 32697, 33633, 35806, 39586, 43737, 44734, 49028, 55345, 56337, 57664, 58306, 62635, 65913, 65975, 66651, 67068, 67729, 69280, 69836, 73616, 73617, 74169

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)
• Eric Weisstein's World of Mathematics, Smith Brothers.

Crossrefs

Cf. A006753, A050219.

Programs

Maple

issmith:= proc(n)
  if isprime(n) then return false fi;
  convert(convert(n,base,10),`+`) = add(t[2]*convert(convert(t[1],base,10),`+`),t=ifactors(n)[2])
end proc:
S:= select(issmith, {$4..10^5}):
sort(convert(S intersect map(`+`,S,1), list)); # Robert Israel, Jan 15 2018

Mathematica

smithQ[n_] := n > 1 && !PrimeQ[n] && Total[Flatten[IntegerDigits[Table[#[[1]], {#[[2]]}]& /@ FactorInteger[n]]]] == Total[IntegerDigits[n]];
Select[Range[10^5], smithQ[#] && smithQ[#-1]&] (* Jean-François Alcover, Jun 07 2020 *)

PARI

isone(n) = {if (!isprime(n), f = factor(n); sumdigits(n) == sum(k=1, #f~, f[k,2]*sumdigits(f[k,1])););}
isok(n) =  isone(n) && isone(n-1); \\ Michel Marcus, Jul 17 2015

Python

from sympy import factorint
from itertools import count, islice
def sd(n): return sum(map(int, str(n)))
def smith():
    for k in count(1):
        f = factorint(k)
        if sum(f[p] for p in f) > 1 and sd(k) == sum(sd(p)*f[p] for p in f):
            yield k
def agen():
    prev = -1
    for s in smith():
        if s == prev + 1: yield s
        prev = s
print(list(islice(agen(), 38))) # Michael S. Branicky, Dec 23 2022

Extensions

Offset corrected by Arkadiusz Wesolowski, May 08 2012