A050219 - OEIS

%I #34 Dec 23 2022 17:25:37

%S 728,2964,3864,4959,5935,6187,9386,9633,11695,13764,16536,16591,20784,

%T 25428,28808,29623,32696,33632,35805,39585,43736,44733,49027,55344,

%U 56336,57663,58305,62634,65912,65974,66650,67067,67728,69279,69835,73615,73616,74168

%N Smaller of Smith brothers.

%H Amiram Eldar, <a href="/A050219/b050219.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert Israel)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmithBrothers.html">Smith Brothers.</a>

%p issmith:= proc(n)

%p   if isprime(n) then return false fi;

%p   convert(convert(n,base,10),`+`) = add(t[2]*convert(convert(t[1],base,10),`+`),t=ifactors(n)[2])

%p end proc:

%p S:= select(issmith, {$4..10^5}):

%p sort(convert(S intersect map(`-`,S,1), list)); # _Robert Israel_, Jan 15 2018

%t smithQ[n_] := !PrimeQ[n] && Total[Flatten[IntegerDigits[Table[#[[1]], {#[[2]]}]& /@ FactorInteger[n]]]] == Total[IntegerDigits[n]];

%t Select[Range[10^5], smithQ[#] && smithQ[#+1]&] (* _Jean-François Alcover_, Jun 07 2020 *)

%o (PARI) isone(n) = {if (!isprime(n), f = factor(n); sumdigits(n) == sum(k=1, #f~, f[k,2]*sumdigits(f[k,1])););}

%o isok(n) =  isone(n) && isone(n+1); \\ _Michel Marcus_, Jul 17 2015

%o (Python)

%o from sympy import factorint

%o from itertools import count, islice

%o def sd(n): return sum(map(int, str(n)))

%o def smith():

%o     for k in count(1):

%o         f = factorint(k)

%o         if sum(f[p] for p in f) > 1 and sd(k) == sum(sd(p)*f[p] for p in f):

%o             yield k

%o def agen():

%o     prev = -1

%o     for s in smith():

%o         if s == prev + 1: yield prev

%o         prev = s

%o print(list(islice(agen(), 38))) # _Michael S. Branicky_, Dec 23 2022

%Y Cf. A006753, A050220.

%K nonn,base

%O 1,1

%A _Eric W. Weisstein_

%E Offset corrected by _Arkadiusz Wesolowski_, May 08 2012