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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).
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, 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)
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 18 2018
STATUS
approved