A061770 Numbers m = a(n) > a(n-1) such that there exists a smallest integer k > 1 such that k!/(k+1)^m is an integer.

0, 1, 2, 5, 7, 8, 9, 10, 11, 14, 17, 19, 21, 28, 35, 44, 58, 88, 95, 103, 110, 178, 179, 185, 208, 222, 287, 313, 334, 358, 371, 419, 479, 502, 558, 629, 670, 718, 838, 1006, 1118, 1259, 1438

Offset: 0

Author

Robert G. Wilson v, Jun 21 2001

Keywords

• nonn

Comments

Original name: The least exponent m = a(n) > a(n-1) for which k is the first number where k!/(k+1)^m is an integer.

Examples

			a(5) = 8 because the first integer k > 1 such that (k+1)^8 divides k! is k = 39, which is larger than the first integer k > 1 such that (k+1)^7 divides k! (k = 35).
6 is not in the sequence because the first integer k > 1 such that (k+1)^6 divides k! is k = 23, which is equal to the first integer k > 1 such that (k+1)^5 divides k!.
		

Crossrefs

Locations of records in A061768.

Programs

Mathematica

l = 0; Do[k = Max[l - 1, 1]; While[ !IntegerQ[ k! / (k + 1)^n], k++ ]; If[ k > l, l = k; Print[n] ], {n, 0, 1500} ]

PARI

b(n)=k=2;while(k!%(k+1)^n,k++);k
print1(0,", ");for(n=1,100,if(b(n)>b(n-1),print1(n,", "))) \\ Derek Orr, Apr 16 2015

Extensions

Name and example edited by Derek Orr, Apr 16 2015