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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A373736 a(n) = largest nondivisor k < n such that A007947(k) | n, or 0 if k does not exist. 1
 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 9, 0, 8, 9, 0, 0, 16, 0, 16, 9, 16, 0, 18, 0, 16, 0, 16, 0, 27, 0, 0, 27, 32, 25, 32, 0, 32, 27, 32, 0, 36, 0, 32, 27, 32, 0, 36, 0, 40, 27, 32, 0, 48, 25, 49, 27, 32, 0, 54, 0, 32, 49, 0, 25, 64, 0, 64, 27, 64, 0, 64, 0, 64, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The number k does not exist for n in A000961, therefore we write a(n) = 0. For n in A024619, a(n) is the largest term in row n of A162306 or A272618. For n in A024619, a(n) is composite, since A007947(p) | n implies p | n for prime p. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 Michael De Vlieger, Scalar scatterplot of a(n) for n = 1..2^20. Michael De Vlieger, Plot a(n) at (x,y) = (n mod 210, -floor(n/210)) for n = 1..44100, showing 0 in light gray, perfect prime powers (a(n) in A246547) in gold, a(n) in A332785 in blue, and a(n) in A286708 in magenta. EXAMPLE Let rad = A007947 and let S(n) = {k <= n : rad(k) | n}, i.e., row n of A162306. a(6) = 4 since 4 is the largest nondivisor k in S(6) = {1, 2, 3, 4, 6}. a(10) = 8 since 8 is the largest nondivisor k in S(10) = {1, 2, 4, 5, 8, 10}. a(15) = 9 since 9 is the largest nondivisor k in S(15) = {1, 3, 5, 9, 15}, etc. MATHEMATICA rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; Table[If[PrimePowerQ[n], 0, k = n - 1; Until[And[Divisible[n, rad[k]], ! Divisible[n, k]], k--]; k], {n, 2, 120}] PROG (PARI) rad(n) = factorback(factorint(n)[, 1]); a(n) = forstep(k=n-1, 1, -1, if ((n % k) && !(n % rad(k)), return(k))); \\ Michel Marcus, Jun 18 2024 CROSSREFS Cf. A000961, A007947, A024619, A162306, A272618. Sequence in context: A285214 A285340 A252798 * A169766 A003194 A350998 Adjacent sequences: A373733 A373734 A373735 * A373737 A373739 A373740 KEYWORD nonn AUTHOR Michael De Vlieger, Jun 18 2024 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 August 6 00:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)