

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



