A243036 -id:A243036 - cp's OEIS frontend

A382291 a(n) = A037445(n)/A034444(n).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Amiram Eldar, Mar 21 2025

First differs from A368168 at n = 64, and from A359411, A367516 and A368979 at n = 128.

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

Cf. A000120, A034444, A037445, A138302, A243036, A382290, A382292.

Cf. A359411, A367516, A368168, A368979.

f[p_, e_] := 2^(DigitCount[e, 2, 1] - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 105]

a(n) = vecprod(apply(x -> 1 << (hammingweight(x)-1), factor(n)[, 2]));

a(n) = 2^A382290(n).
Multiplicative with a(p^e) = 2^(A000120(e)-1) = A048896(e-1) (= A243036(e) for e >= 2).
a(n) >= 1, with equality if and only if n is in A138302.
a(n) = 2 if and only if n is in A382292.

A243035 Number of entries of length n in A240601.

Original entry on oeis.org

10, 9, 90, 9, 90, 90, 900, 9, 90, 90, 900, 90, 900, 900, 9000, 9, 90, 90, 900, 90, 900, 900, 9000, 90, 900, 900, 9000, 900, 9000, 9000, 90000, 9, 90, 90, 900, 90, 900, 900, 9000, 90, 900, 900, 9000, 900, 9000, 9000, 90000, 90, 900, 900, 9000, 900, 9000, 9000

Offset: 1

Lior Manor, May 29 2014

For n>0, a(2^n) = 9.
For any base b, a(1) = b, a(2) = b-1, a(3) = b*(b-1), for m>1, a(2m) = a(m), a(2m+1) = b*a(m).
For any base b, a(n) = (b-1)*b^(A000120(n)-1).

Cf. A240601, A243036, A000120.

a(1) = 10, a(2) = 9, a(3) = 90, For m>1, a(2m) = a(m), a(2m+1) = 10*a(m).

a(n) = 9*10^(A000120(n)-1).

cp's OEIS Frontend

A382291 a(n) = A037445(n)/A034444(n).

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