A006146 Sums of prime divisors of Ruth-Aaron numbers (A006145).

5, 5, 7, 18, 15, 20, 44, 46, 29, 31, 50, 30, 20, 34, 75, 162, 146, 46, 14, 113, 53, 66, 333, 36, 514, 318, 43, 193, 279, 418, 30, 121, 55, 485, 200, 136, 77, 37, 211, 587, 147, 269, 477, 108, 136, 235, 185, 290, 333, 309, 493, 177, 199, 223, 641, 531, 182, 368

Offset

1,1

References

John L. Drost, Ruth/Aaron Pairs, J. Recreational Math. 28 (No. 2), 120-122.

Dana Mackenzie, Homage to an itinerant master, Science, vol. 275, p. 759, 1997.

Carol Nelson, David E. Penney, and Carl Pomerance, 714 and 715. Journal of Recreational Mathematics 7(2):87-89, 1974.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonné, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74. (Annotated scanned copy)

Ivars Peterson, Playing with Ruth-Aaron pairs

Ivars Peterson's MathTrek, Playing with Ruth-Aaron Pairs [In the internet archive]

Eric Weisstein's World of Mathematics, Ruth-Aaron Pair

Formula

a(n) = A008472(A006145(n)) = A008472(A006145(n) + 1). - Amiram Eldar, Nov 24 2019

Maple

with(numtheory): for n from 1 to 10000 do t0 := 0; t1 := factorset(n);
for j from 1 to nops(t1) do t0 := t0+t1[ j ]; od: s[ n ] := t0; od:
for n from 1 to 9999 do if s[ n ] = s[ n+1 ] then lprint(n, s[ n ]); fi; od:

Mathematica

Cases[Partition[(Plus@@(First@#&/@FactorInteger@#)&/@Range@100000), 2, 1], {a_, a_}:>a] (* Hans Rudolf Widmer, May 31 2024 *)

Prog

(Python)
from sympy import primefactors
def aupton(terms):
  alst, k, sopfk, sopfkp1 = [], 0, 0, 1
  while len(alst) < terms:
    k, sopfk, sopfkp1 = k+1, sopfkp1, sum(p for p in primefactors(k+1))
    if sopfkp1 == sopfk: alst.append(sopfk)
  return alst
print(aupton(58)) # Michael S. Branicky, May 05 2021

Crossrefs

Cf. A006145, A008472, A039752, A039753, A039703, A054378.

Sequence in context: A088047 A109257 A088048 * A284129 A077956 A077977

Adjacent sequences: A006143 A006144 A006145 * A006147 A006148 A006149

Keyword

nonn

Author

N. J. A. Sloane

Status

approved