A045759 Maris-McGwire numbers: numbers k such that f(k) = f(k+1), where f(k) = sum of digits of k + sum of digits of prime factors of k (including multiplicities).

7, 14, 43, 50, 61, 63, 67, 80, 84, 118, 122, 134, 137, 163, 196, 212, 213, 224, 241, 273, 274, 277, 279, 283, 351, 352, 373, 375, 390, 398, 421, 457, 462, 474, 475, 489, 495, 510, 516, 523, 526, 537, 547, 555, 558, 577, 584, 590, 592, 616, 638, 644, 660, 673, 687, 691

Offset: 1

Author

Mike Keith

Keywords

• nonn
• base

Comments

Named "Maris-McGwire-Sosa Numbers" by Keith (1998) after the baseball players Roger Maris, Mark McGwire and Sammy Sosa. Both McGwire and Sosa hit their 62nd home runs for the season, breaking Maris's record of 61 (A006145 is a similarly named sequence). - Amiram Eldar, Jun 27 2021

Examples

			(61, 62) is such a pair, hence the name.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Mike Keith, Maris-McGwire-Sosa Numbers, 1998.
• Ivars Peterson, Home Run Numbers, MathTrek, 1998.
• Wikipedia, Maris-McGwire-Sosa pair.

Crossrefs

Cf. A006145 (Ruth-Aaron numbers), A039945.

Programs

Mathematica

ds[n_] := Plus @@ IntegerDigits[n]; f[n_] := ds[n] + Total[(fi = FactorInteger[n])[[;; , 2]] *( ds /@fi[[;; , 1]])]; s={}; f1 = 1; Do[f2=f[n]; If[f1 == f2, AppendTo[s, n-1]]; f1 = f2, {n, 2, 700}]; s (* Amiram Eldar, Nov 24 2019 *)

Python

from sympy import factorint
def sd(n): return sum(map(int, str(n)))
def  f(n): return sd(n) + sum(sd(p)*e for p, e in factorint(n).items())
def ok(n): return f(n) == f(n+1)
print(list(filter(ok, range(692)))) # Michael S. Branicky, Jul 14 2021

Extensions

Corrected and extended by David W. Wilson

Offset corrected by Amiram Eldar, Nov 24 2019