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A294905
Characteristic function for A000120-nonabundant numbers: a(n) = 1 if A292257(n) <= A000120(n), and 0 otherwise.
7
1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1
OFFSET
1
FORMULA
a(n) = 1 if A192895(n) <= 0, and 0 otherwise.
a(n) = [A292257(n) <= A000120(n)].
EXAMPLE
For n=25, its proper divisors are 1 and 5, in binary "1" and "101", so the total number of 1's in them is 3, while 25 in binary is "11001", with binary weight 3, thus as A292257(25) <= A000120(25), a(25) = 1.
For n=55, its proper divisors are 1, 5 and 11, in binary "1", "101" and "1011", so the total number of 1's in them is 6, while 55 in binary is "110111", with binary weight 5, thus as A292257(55) > A000120(55), a(55) = 0.
MATHEMATICA
a[n_] := If[DivisorSum[n, DigitCount[#, 2, 1] &] > 2 * DigitCount[n, 2, 1], 0, 1]; Array[a, 100] (* Amiram Eldar, Jul 20 2023 *)
PROG
(PARI)
A292257(n) = sumdiv(n, d, (d<n)*hammingweight(d));
A294905(n) = (A292257(n) <= hammingweight(n));
CROSSREFS
Cf. A175526 (positions of zeros), A257691 (of ones).
After n=1, differs from A010051 for the next time at n=25, and from both A283991 and A257000 at n=55.
Sequence in context: A192490 A267133 A080339 * A353787 A297086 A349920
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Nov 10 2017
STATUS
approved