A177900 Smallest positive integer k such that the sum of the proper divisors of k gives the n-th prime, or 0 if prime(n) belongs to A005114.

0, 4, 0, 8, 21, 27, 39, 65, 57, 115, 32, 155, 63, 50, 129, 235, 265, 371, 305, 201, 98, 365, 237, 171, 245, 291, 485, 309, 325, 327, 128, 189, 279, 917, 1507, 1529, 242, 785, 489, 835, 865, 1211, 385, 605, 579, 965, 338, 2321, 669, 1115, 687, 1165, 399, 2629, 549, 1285, 595, 1841, 1025, 603, 1385, 715, 3809, 921, 1175, 939, 4121, 1655, 805, 1325

Offset

1,2

Comments

Suggested by the following comment of T. D. Noe (see A037020): "Assuming the Goldbach conjecture, it is easy to show that all primes, except 2 and 5, are the sum of the proper divisors of some number."

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Formula

a(n) = A070015(p_n) where p runs through the primes. - Robert G. Wilson v, Jul 09 2014

Example

27 and 35 have the proper divisors {1,3,9} and {1,5,7}, respectively, both of which sum to prime(6)=13, and no positive integer smaller than 27 has this property.  Thus a(6)=27.

Maple

N:= 1000: # to get the first N terms
A:= 'A': A[1]:= 0: A[3]:= 0:
Primes:= [seq(ithprime(i), i=1..N)]:
count:= 0:
for k from 1  while count < N-2 do
  m:= numtheory:-sigma(k)-k;
  if member(m, Primes, 'n') and not assigned(A[n]) then
     count:= count+1;
     A[n]:= k;
  fi
od:
seq(A[i], i=1..N); # Robert Israel, Jul 09 2014

Mathematica

f[n_] := DivisorSigma[1, n] - n; k = 1; t = Table[0, {1000}]; While[ k < 24001, a = f@ k; If[a < 1001 && t[[a]] == 0, t[[a]] = k]; k++]; tt = Table[t[[n]], {n, Prime@ Range@ 168}] (* Robert G. Wilson v, Jul 09 2014 *)

Prog

(PARI) a(n) = {p = prime(n); if ((p != 2) && (p != 5), k = 2; while ((sigma(k) - k) != p, k++); k; ); } \\ Michel Marcus, Jul 09 2014

Crossrefs

Cf. A037020, A005114.

Sequence in context: A324482 A216406 A152990 * A214202 A019249 A260491

Adjacent sequences: A177897 A177898 A177899 * A177901 A177902 A177903

Keyword

nonn

Author

John W. Layman, Dec 15 2010

Extensions

Offset corrected to 1 by Michel Marcus, Jul 09 2014

Status

approved