A077542 Least number of terms required in the product (k+1)(k+2)... to make it a multiple of the product of next n number, where k = n(n+1)/2.

1, 3, 4, 6, 6, 7, 11, 10, 10, 13, 14, 17, 14, 20, 25, 19, 21, 19, 32, 24, 28, 34, 25, 33, 27, 36, 46, 35, 42, 31, 53, 36, 49, 54, 41, 44, 39, 63, 46, 56, 62, 51, 59, 54, 71, 81, 57, 70, 56, 83, 88, 77, 84, 67, 95, 69, 98, 97, 84, 96, 71, 84, 75, 100, 102, 78, 95, 79, 125

Offset

1,2

Comments

For n > 5, a(n) >= 2p - n, where p is the largest prime less than n(n+1)/2.

Links

Table of n, a(n) for n=1..69.

Formula

Let A077540(n) = (k+1)(k+2)...(k+r) where k = n(n+1)/2 then a(n) = r.

Example

a(3) = 4 as A077540(3) = 5040 = 7*8*9*10 = (6+1)(6+2)(6+3)(6+4).

Prog

(PARI) for(n=1, 100, p=1:t=n*(n+1)/2:f=1:for(k=1, n, f=f*(n+k)):for(k=1, 10^9, p=p*(t+k): if(p%f==0, print1(k", "):break)))

Crossrefs

Cf. A077540, A077541.

Sequence in context: A135319 A329193 A004219 * A325611 A263842 A286956

Adjacent sequences: A077539 A077540 A077541 * A077543 A077544 A077545

Keyword

nonn

Author

Amarnath Murthy, Nov 09 2002

Extensions

Corrected and extended by Ralf Stephan, Mar 27 2003

Status

approved