

A093451


Number of distinct prime divisors of Product_{k=1+(n1)n/2..n(n+1)/2)} k (i.e., of 1, 2*3, 4*5*6, 7*8*9*10, ...).


2



0, 2, 3, 4, 6, 6, 7, 8, 10, 10, 11, 13, 13, 14, 16, 15, 18, 17, 20, 19, 22, 21, 22, 24, 24, 26, 26, 27, 30, 28, 30, 31, 32, 33, 33, 36, 35, 36, 38, 39, 39, 39, 43, 41, 43, 44, 44, 47, 45, 49, 48, 48, 52, 49, 53, 53, 54, 54, 55, 58, 55, 60, 59, 59, 62, 60, 65, 64, 64, 65, 66, 68
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..72.


FORMULA

a(n) = A001221(A057003(n)).  Michel Marcus, Jul 29 2017


EXAMPLE

a(7) = 7 as the prime divisors of the product 22*23*24*25*26*27*28 are 2,3,5,7,11,13 and 23.


MAPLE

with(numtheory): a:=n>nops(factorset(product(k, k=1+n*(n1)/2..n*(n+1)/2))): seq(a(n), n=1..80); # Emeric Deutsch, Feb 05 2006


CROSSREFS

Cf. A001221, A057003.
Sequence in context: A154257 A297351 A060019 * A106006 A050460 A246594
Adjacent sequences: A093448 A093449 A093450 * A093452 A093453 A093454


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Apr 03 2004


EXTENSIONS

Corrected and extended by Emeric Deutsch, Feb 05 2006


STATUS

approved



