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A367933
a(n) is the smallest multiple of n that is an exponentially odious number (A270428).
3
1, 2, 3, 4, 5, 6, 7, 16, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 48, 25, 26, 81, 28, 29, 30, 31, 128, 33, 34, 35, 36, 37, 38, 39, 80, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 162, 55, 112, 57, 58, 59, 60, 61, 62, 63, 128, 65, 66, 67
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = p^s(e), s(e) = min{k >= e, k is odious}.
a(n) = n * A367931(n).
a(n) >= n, with equality if and only if n is an exponentially odious number (A209061).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} f(1/p) = 1.30023300... , where f(x) = (1-x) * (1 + Sum_{k>=1} x^(2*k-s(k))), and s(k) is defined above.
MATHEMATICA
f[p_, e_] := Module[{k = e}, While[! OddQ[DigitCount[k, 2 , 1]], k++]; p^k]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(e) = {my(k = e); while(!(hammingweight(k)%2), k++); k; };
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }
CROSSREFS
Similar sequences: A356192, A365684, A367934.
Sequence in context: A055402 A274839 A361809 * A356194 A065640 A264974
KEYWORD
nonn,easy,mult,base
AUTHOR
Amiram Eldar, Dec 05 2023
STATUS
approved