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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).
3
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
1,1
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
LINKS
Mike Keith, Maris-McGwire-Sosa Numbers, 1998.
Ivars Peterson, Home Run Numbers, MathTrek, 1998.
EXAMPLE
(61, 62) is such a pair, hence the name.
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 *)
PROG
(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
CROSSREFS
Cf. A006145 (Ruth-Aaron numbers), A039945.
Sequence in context: A098328 A062098 A374509 * A166637 A237686 A170918
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Corrected and extended by David W. Wilson
Offset corrected by Amiram Eldar, Nov 24 2019
STATUS
approved