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
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
KEYWORD
nonn
AUTHOR
STATUS
approved