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A366903
The sum of exponentially odious divisors of n.
5
1, 3, 4, 7, 6, 12, 8, 7, 13, 18, 12, 28, 14, 24, 24, 23, 18, 39, 20, 42, 32, 36, 24, 28, 31, 42, 13, 56, 30, 72, 32, 23, 48, 54, 48, 91, 38, 60, 56, 42, 42, 96, 44, 84, 78, 72, 48, 92, 57, 93, 72, 98, 54, 39, 72, 56, 80, 90, 60, 168, 62, 96, 104, 23, 84, 144, 68
OFFSET
1,2
COMMENTS
First differs from A353900 at n = 128.
The number of these divisors is A366901(n) and the largest of them is A366905(n).
LINKS
FORMULA
Multiplicative with a(p^e) = 1 + Sum_{k = 1..e, k is odious} p^k.
a(n) <= A000203(n), with equality if and only if n is a cubefree number (A004709).
Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1-1/p)*(1 + Sum_{k>=1} a(p^k)/p^(2*k)) = 0.721190607... .
MATHEMATICA
f[p_, e_] := 1 + Total[p^Select[Range[e], OddQ[DigitCount[#, 2, 1]] &]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(k = 1, f[i, 2], (hammingweight(k)%2) * f[i, 1]^k)); }
CROSSREFS
Similar sequences: A353900, A365682, A366904.
Sequence in context: A377520 A073183 A353900 * A049418 A333926 A051378
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 27 2023
STATUS
approved