The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A360316 a(n) is the smallest k such that k!'s prime(n)-smooth part is less than its prime(n+1)-rough part. 0
 3, 21, 47, 111, 186, 293, 437, 619, 830, 1070, 1358, 1662, 2019, 2428, 2903, 3373, 3908, 4493, 5113, 5791, 6506, 7325, 8150, 9043, 9942, 10929, 11983, 13089, 14303, 15591, 16845, 18143, 19535, 21003, 22488, 24046, 25693, 27333, 29119, 30905, 32741, 34764, 36734 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..43. EXAMPLE For n=1, the prime(1)-smooth part of k! (i.e., the 2-smooth part) is the part whose prime factors are 2's; the prime(2)-rough part (i.e., the 3-rough part) is the odd part. For k = 1..3, we have k k! 2-smooth part 3-rough part - -- ------------- ------------ 1 1 1 = 1 2 2 2 > 1 3 6 2 < 3 so a(1)=3. Similarly, for n=2, we have k 3-smooth part 5-rough part -- ------------- ------------ 1 1 = 1 2 2 > 1 3 6 > 1 4 24 > 1 5 24 > 5 . . . . . . . . 18 429981696 > 14889875 19 429981696 > 282907625 20 1719926784 > 1414538125 21 5159780352 < 9901766875 so a(2)=21. CROSSREFS Cf. A000142. Sequence in context: A364051 A318549 A217000 * A034186 A318211 A219069 Adjacent sequences: A360313 A360314 A360315 * A360317 A360318 A360319 KEYWORD nonn AUTHOR Jon E. Schoenfield, Feb 03 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 14:29 EST 2023. Contains 367540 sequences. (Running on oeis4.)