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

1, 3, 4, 6, 11, 17, 18, 26, 41, 51, 56, 68, 87, 101, 106, 126, 149, 163, 172, 188, 227, 249, 266, 286, 309, 347, 368, 396, 431, 461, 486, 518, 553, 591, 608, 656, 699, 737, 766, 802, 857, 871, 936, 976, 1031, 1057, 1118, 1166, 1221, 1243, 1316, 1368, 1427

Offset

1,2

Links

Table of n, a(n) for n=1..53.

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) m=1; for(n=1, 100, p=1; t=n*(n+1)/2; f=1; for(k=1, n, f=f*m; m=m+1); for(k=1, 10^9, p=p*(t+k); if(p%f==0, print1(k", "); break))) \\ [Updated by Sean A. Irvine, May 28 2025]

Crossrefs

Cf. A077540, A077541.

Sequence in context: A154331 A001130 A348529 * A069825 A093040 A022935

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

a(5) onward corrected by Sean A. Irvine, May 28 2025

Status

approved