A227654 Ruth-Aaron triples (1): sum of primes dividing n = sum of primes dividing (n+1) = sum of primes dividing (n+2).

89460294, 151165960539, 3089285427491, 6999761340223, 7539504384825

Offset: 1

Author

Giovanni Resta, Jul 19 2013

Keywords

• nonn
• hard
• more

Comments

a(6) > 10^13. Taking into account primes multiplicity (A039752), the only triples up to 10^13 are those starting at 417162 and 6913943284.

Examples

			7539504384825 = 3^2 * 5^2 * 7^2 * 43 * 251 * 63361,
7539504384826 = 2 * 19 * 367 * 10181 * 53101,
7539504384827 = 17 * 457 * 26309 * 36887 and
3 + 5 + 7 + 43 + 251 + 63361 = 2 + 19 + 367 + 10181 + 53101 = 17 + 457 + 26309 + 36887.
		

Links

• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.
• Carlos Rivera, Puzzle 358. Ruth-Aaron Pairs Revisited, The Prime Puzzles and Problems Connection.
• Eric Weisstein's World of Mathematics, Ruth-Aaron Pair.
• Wikipedia, Ruth-Aaron pair.

Crossrefs

Cf. A006145, A039752.