A050219 Smaller of Smith brothers.
728, 2964, 3864, 4959, 5935, 6187, 9386, 9633, 11695, 13764, 16536, 16591, 20784, 25428, 28808, 29623, 32696, 33632, 35805, 39585, 43736, 44733, 49027, 55344, 56336, 57663, 58305, 62634, 65912, 65974, 66650, 67067, 67728, 69279, 69835, 73615, 73616, 74168
Offset: 1
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.
Programs
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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_] := !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 prev prev = s print(list(islice(agen(), 38))) # Michael S. Branicky, Dec 23 2022
Extensions
Offset corrected by Arkadiusz Wesolowski, May 08 2012