

A023846


Sum of exponents in primepower factorization of binomial(5n, n+4).


1



0, 4, 5, 6, 6, 8, 10, 10, 10, 11, 12, 13, 15, 14, 14, 16, 15, 17, 16, 20, 19, 18, 18, 20, 19, 22, 25, 22, 23, 25, 24, 26, 24, 25, 24, 26, 25, 27, 30, 30, 28, 31, 29, 29, 31, 29, 31, 33, 32, 33, 33, 37, 36, 38, 39, 40, 38, 42, 40, 41, 40, 39, 39, 40, 39, 40, 39, 40, 43, 41, 43, 47, 43, 45, 47, 45, 46
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OFFSET

1,2


COMMENTS

By Kummer's theorem, a(n) is the sum over all primes p of the number of carries when n+4 is added to 4n4 in base p.  Robert Israel, Nov 09 2017


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000
Wikipedia, Kummer's theorem


MAPLE

seq(numtheory:bigomega(binomial(5*n, n+4)), n=1..100); # Robert Israel, Nov 09 2017


MATHEMATICA

Table[PrimeOmega[Binomial[5 n, n + 4]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)


PROG

(PARI) a(n) = a(n) = bigomega(binomial(5*n, n+4)); \\ Michel Marcus, Nov 09 2017


CROSSREFS

Cf. A023816A023854.
Sequence in context: A162310 A116962 A273777 * A046345 A325103 A004445
Adjacent sequences: A023843 A023844 A023845 * A023847 A023848 A023849


KEYWORD

nonn


AUTHOR

Clark Kimberling


STATUS

approved



