The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303545 For any n > 0 and prime number p, let d_p(n) be the distance from n to the nearest p-smooth number; a(n) = Sum_{i prime} d_i(n). 5
 0, 0, 1, 0, 2, 2, 3, 0, 1, 3, 6, 4, 7, 5, 2, 0, 6, 2, 9, 6, 9, 11, 14, 8, 8, 10, 5, 6, 12, 4, 10, 0, 4, 9, 5, 4, 15, 16, 13, 12, 24, 18, 28, 18, 16, 22, 28, 16, 17, 16, 20, 20, 25, 10, 12, 12, 17, 22, 24, 8, 21, 13, 3, 0, 5, 8, 26, 18, 16, 10, 25, 8, 28, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS For any n > 0 and prime number p >= A006530(n), d_p(n) = 0; hence the series in the name contains only finitely many nonzero terms and is well defined. See also A303548 for a similar sequence. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..32768 Rémy Sigrist, Colored pin plot of the first 3 * 512 terms (where the color is function of the prime p in the term d_p(n)) Index entries for sequences related to distance to nearest element of some set FORMULA a(n) = 0 iff n is a power of 2. a(2 * n) <= 2 * a(n). a(n) >= A053646(n) + A301574(n) (as d_2 = A053646 and d_3 = A301574). EXAMPLE For n = 42: - d_2(42) = |42 - 32| = 10, - d_3(42) = |42 - 36| = |42 - 48| = 6, - d_5(42) = |42 - 40| = 2, - d_p(42) = 0 for any prime number p >= 7, - hence a(42) = 10 + 6 + 2 = 18. PROG (PARI) gpf(n) = if (n==1, 1, my (f=factor(n)); f[#f~, 1]) a(n) = my (v=0, pi=primepi(gpf(n))); for (d=0, oo, my (o=min(primepi(gpf(n-d)), primepi(gpf(n+d)))); if (o

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 May 22 17:00 EDT 2024. Contains 372758 sequences. (Running on oeis4.)