A357478 Numbers n such that both n and n+1 are in A175729.
7105, 37583, 229177, 309281, 343865, 480654, 794625, 808860, 977185, 2135895, 2174080, 2755841, 5978490, 6865055, 7147761, 8784216, 11207889, 15251713, 15854166, 21526897, 28432040, 29831601, 32865300, 33531212, 40931731, 53237184, 57766731, 63564985, 67849950, 70751360, 72352760, 85121596
Offset: 1
Keywords
Examples
a(3) = 229177 is a term because 229177 = 13*17^2*61, 13+17+17+61 = 108 divides 229177-1 = 229176, 229177+1 = 229178 = 2*19*37*163, and 2+19+37+163 = 221 divides 229177.
Links
- Robert Israel, Table of n, a(n) for n = 1..75
Crossrefs
Cf. A175729.
Programs
-
Maple
R:= NULL: count:= 0: state:= 0: for n from 2 while count < 30 do s:= add(t[1]*t[2],t=ifactors(n)[2]); if n mod s = 1 then if state = 1 then R:= R, n-1; count:= count+1 fi; state:= 1; else state:= 0; fi od: R; -
Mathematica
q[n_] := Divisible[n - 1, Plus @@ Times @@@ FactorInteger[n]]; s = {}; q1 = q[2]; Do[q2 = q[n]; If[q1 && q2, AppendTo[s, n - 1]]; q1 = q2, {n, 3, 10^6}]; s (* Amiram Eldar, Sep 30 2022 *) -
Python
from sympy import factorint from itertools import count, islice def ok(n): return n > 1 and (n-1)%sum(p*e for p, e in factorint(n).items()) == 0 def agen(): prevok = kok = False for k in count(1): prevok, kok = kok, ok(k) if prevok and kok: yield k-1 print(list(islice(agen(), 6))) # Michael S. Branicky, Sep 30 2022
Comments