A367934 a(n) is the smallest multiple of n that is an exponentially evil number (A262675).

1, 8, 27, 8, 125, 216, 343, 8, 27, 1000, 1331, 216, 2197, 2744, 3375, 32, 4913, 216, 6859, 1000, 9261, 10648, 12167, 216, 125, 17576, 27, 2744, 24389, 27000, 29791, 32, 35937, 39304, 42875, 216, 50653, 54872, 59319, 1000, 68921, 74088, 79507, 10648, 3375, 97336

Offset

1,2

Comments

First differs from A356192 at n = 64.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = p^s(e), s(e) = min{k >= e, k is evil}.

a(n) = n * A367932(n).

a(n) >= n, with equality if and only if n is an exponentially evil number (A262675).

Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = Product_{p prime} f(1/p) = 0.623746285..., where f(x) = (1-x) * (1 + Sum_{k>=1} x^(4*k-s(k))), and s(k) is defined above.

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^s(k)) = 1.70170328791367919805... .

Mathematica

f[p_, e_] := Module[{k = e}, While[! EvenQ[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

Cf. A262675, A367932.

Similar sequences: A356192, A365684, A367933.

Sequence in context: A056551 A356193 A356192 * A053149 A102637 A250140

Adjacent sequences: A367931 A367932 A367933 * A367935 A367936 A367937

Keyword

nonn,easy,mult,base

Author

Amiram Eldar, Dec 05 2023

Status

approved