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

1,1

Comments

Numbers n such that the sum of the prime factors with multiplicity of n divides n-1 and the sum of the prime factors with multiplicity of n+1 divides n.

Links

Robert Israel, Table of n, a(n) for n = 1..75

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A175729.

Sequence in context: A235194 A034230 A183630 * A189354 A252383 A252350

Adjacent sequences: A357475 A357476 A357477 * A357479 A357480 A357481

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 30 2022

Status

approved