A295368 For any number n > 0 with s divisors, say d_1, d_2, ..., d_s such that d_1 = 1 < d_2 < ... < d_s = n, the binary representation of a(n) is (d_1 mod 2, d_2 mod 2, ..., d_s mod 2).

1, 2, 3, 4, 3, 10, 3, 8, 7, 10, 3, 40, 3, 10, 15, 16, 3, 42, 3, 36, 15, 10, 3, 160, 7, 10, 15, 36, 3, 178, 3, 32, 15, 10, 15, 328, 3, 10, 15, 144, 3, 170, 3, 36, 63, 10, 3, 640, 7, 42, 15, 36, 3, 170, 15, 144, 15, 10, 3, 2696, 3, 10, 63, 64, 15, 170, 3, 36, 15

Offset

1,2

Comments

This sequence encodes in binary the parity of the divisors of a number.

For any n > 0, the binary representation of a(n) corresponds to the n-th row of A247795.

For any n > 0, n and a(n) have the same parity.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A000005(n))

Formula

a(2^k) = 2^k for any k >= 0.

a(p) = 3 iff p is an odd prime.

a(n) > 3 iff n is composite.

A070939(a(n)) = A000005(n) for any n > 0.

A000120(a(n)) = A001227(n) for any n > 0.

A023416(a(n)) = A183063(n) for any n > 0.

A000120(a(n)) = A023416(a(n)) iff n belongs to A016825.

Mathematica

Array[FromDigits[Mod[#, 2] & /@ Divisors@ #, 2] &, 69] (* Michael De Vlieger, Feb 18 2018 *)

Prog

(PARI) a(n) = fromdigits(apply(d -> d%2, divisors(n)), 2)

Crossrefs

Cf. A000005, A000120, A001227, A016825, A023416, A070939, A183063, A247795.

Sequence in context: A324195 A339663 A211507 * A283832 A102086 A009184

Adjacent sequences: A295365 A295366 A295367 * A295369 A295370 A295371

Keyword

nonn,base

Author

Rémy Sigrist, Feb 18 2018

Status

approved