|
|
A093451
|
|
Number of distinct prime divisors of Product_{k=1+(n-1)n/2..n(n+1)/2} k (i.e., of 1, 2*3, 4*5*6, 7*8*9*10, ...).
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
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*(n-1)/2..n*(n+1)/2))): seq(a(n), n=1..80); # Emeric Deutsch, Feb 05 2006
|
|
MATHEMATICA
|
With[{nn=75}, PrimeNu[#]&/@Times@@@TakeList[Range[(nn(nn+1))/2], Range[ nn]]] (* Harvey P. Dale, Sep 01 2021 *)
|
|
PROG
|
(PARI) a(n) = { my(b=binomial(n, 2)+1, bp1=binomial(n+1, 2), res = primepi(n)); forprime(p = n + 1, bp1, bp = b%p; if(bp > bp1 % p || bp == 0, res++ ) ); res } \\ David A. Corneth, Sep 01 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|