OFFSET
0,3
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.
EXAMPLE
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!.
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} ]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 21 2001
EXTENSIONS
Name and example edited by Derek Orr, Apr 16 2015
STATUS
approved