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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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 Locations of records in A061768. Sequence in context: A154848 A195997 A186277 * A210449 A080639 A186306 Adjacent sequences:  A061767 A061768 A061769 * A061771 A061772 A061773 KEYWORD nonn AUTHOR Robert G. Wilson v, Jun 21 2001 EXTENSIONS Name and example edited by Derek Orr, Apr 16 2015 STATUS approved

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Last modified February 20 04:38 EST 2020. Contains 332063 sequences. (Running on oeis4.)