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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A006753, A050219.

Sequence in context: A139308 A295024 A167728 * A236334 A232286 A219133

Adjacent sequences: A050217 A050218 A050219 * A050221 A050222 A050223

Keyword

nonn,base

Author

Eric W. Weisstein

Extensions

Offset corrected by Arkadiusz Wesolowski, May 08 2012

Status

approved