This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A306352 a(n) is the least k >= 0 such that all the positive divisors of n have a distinct value under the mapping d -> d AND k (where AND denotes the bitwise AND operator). 1
 0, 1, 2, 3, 4, 7, 2, 7, 10, 13, 2, 15, 4, 5, 6, 15, 16, 31, 2, 29, 6, 7, 2, 31, 12, 9, 10, 11, 4, 15, 2, 31, 42, 49, 6, 63, 4, 7, 6, 63, 8, 15, 2, 14, 14, 5, 2, 63, 18, 29, 18, 21, 4, 31, 6, 23, 18, 9, 2, 31, 4, 5, 14, 63, 76, 127, 2, 115, 6, 15, 2, 127, 8, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This sequence has similarities with A167234. Will every nonnegative integer appear in the sequence? LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, Colored logarithmic scatterplot of the sequence for n = 1..2^19 (where the color is function of floor(n / 2^A070939(a(n)))). FORMULA a(2^k) = 2^k - 1 for any k >= 0. a(n) = 2 iff n belongs to A002145. a(n) <= A218388(n). a(n) AND A218388(n) = a(n). A000120(a(n)) = 1 iff n is a prime number. Apparently: - a(3^k) belongs to A131130 for any k > 0, - a(5^k) belongs to A028399 for any k >= 0. EXAMPLE For n = 15: - the divisors of 15 are: 1, 3, 5 and 15, - their values under the mapping d -> d AND k for k = 0..6 are:   k\d|  1  3  5  15   ---+-------------     0|  0  0  0  0     1|  1  1  1  1     2|  0  2  0  2     3|  1  3  1  3     4|  0  0  4  4     5|  1  1  5  5     6|  0  2  4  6 - the first row with 4 distinct values corresponds to k = 6, - hence a(15) = 6. PROG (PARI) a(n) = my (d=divisors(n)); for (m=0, oo, if (#Set(apply(v -> bitand(v, m), d))==#d, return (m))) CROSSREFS Cf. A000120, A002145, A028399, A070939, A131130, A167234, A218388. Sequence in context: A021903 A274767 A058315 * A072717 A139072 A021430 Adjacent sequences:  A306349 A306350 A306351 * A306353 A306354 A306355 KEYWORD nonn,base AUTHOR Rémy Sigrist, Feb 09 2019 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 December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)