The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A289280 a(n) = least integer k > n such that any prime factor of k is also a prime factor of n. 3
 4, 9, 8, 25, 8, 49, 16, 27, 16, 121, 16, 169, 16, 25, 32, 289, 24, 361, 25, 27, 32, 529, 27, 125, 32, 81, 32, 841, 32, 961, 64, 81, 64, 49, 48, 1369, 64, 81, 50, 1681, 48, 1849, 64, 75, 64, 2209, 54, 343, 64, 81, 64, 2809, 64, 121, 64, 81, 64, 3481, 64, 3721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS In other words: - a(n) is the least k > n such that rad(k) divides rad(n), where rad = A007947, - or, if P_n denotes the set of prime factors of n, then a(n) is the least P_n-smooth number > n. For any n > 1, n < a(n) <= n*lpf(n), where lpf = A020639. a(p^k) = p^(k+1) for any prime p and k > 0. a(n) is never squarefree. This sequence has connections with A079277: - here we search the least P_n-smooth number > n, there the largest < n, - also, if omega(n) > 1 (where omega = A001221),   then n/lpf(n) < A001221(n) < n,   so n < A001221(n)*lpf(n) < n*lpf(n),   as A001221(n)*lpf(n) is P_n-smooth,   we have a(n) <= A001221(n)*lpf(n) < n*lpf(n),   and n cannot divide a(n). The (logarithmic) scatterplot of the sequence has horizontal rays similar to those observed for A079277; they correspond to frequent values, typically with a small number of distinct prime divisors (see also scatterplots in Links section). Given n < a(n) <= n*lpf(n), a(n) | n^m with m >= 2. Values of m: {2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 5, 2, 3, 2, ...}. - Michael De Vlieger, Jul 02 2017 LINKS Rémy Sigrist, Table of n, a(n) for n = 2..10000 Rémy Sigrist, PARI program for A289280 Rémy Sigrist, Logarithmic scatterplot of the first 100000 terms EXAMPLE For n = 42: - 42 = 2 * 3 * 7, hence P_42 = { 2, 3, 7 }, - the P_42-smooth numbers are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 49, ... - hence a(42) = 48. From Michael De Vlieger, Jul 02 2017: (Start) a(n) divides n^m with m >= 2:    n   a(n)    m    2     4     2    3     9     2    4     8     2    5    25     2    6     8     3    7    49     2    8    16     2    9    27     2   10    16     4   11   121     2   12    16     2   13   169     2   14    16     4   15    25     2   16    32     2   17   289     2   18    24     3   19   361     2   20    25     2 (End) MATHEMATICA Table[Which[PrimeQ@ n, n^2, PrimePowerQ@ n, Block[{p = 2, e}, While[Set[e, IntegerExponent[n, p]] == 0, p = NextPrime@ p]; p^(e + 1)], True, Block[{k = n + 1}, While[PowerMod[n, k, k] != 0, k++]; k]], {n, 2, 61}] (* Michael De Vlieger, Jul 02 2017 *) PROG See Links section. CROSSREFS Cf. A001221, A007947, A020639, A079277. Sequence in context: A316346 A135718 A140580 * A077662 A063718 A063748 Adjacent sequences:  A289277 A289278 A289279 * A289281 A289282 A289283 KEYWORD nonn AUTHOR Rémy Sigrist, Jul 01 2017 STATUS approved

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

Last modified October 16 10:19 EDT 2021. Contains 348041 sequences. (Running on oeis4.)