A053149 -id:A053149 - cp's OEIS frontend

A372329 a(n) is the smallest multiple of n whose number of divisors is a power of 2 (A036537).

1, 2, 3, 8, 5, 6, 7, 8, 27, 10, 11, 24, 13, 14, 15, 128, 17, 54, 19, 40, 21, 22, 23, 24, 125, 26, 27, 56, 29, 30, 31, 128, 33, 34, 35, 216, 37, 38, 39, 40, 41, 42, 43, 88, 135, 46, 47, 384, 343, 250, 51, 104, 53, 54, 55, 56, 57, 58, 59, 120, 61, 62, 189, 128, 65

Offset: 1

Amiram Eldar, Apr 28 2024

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

Cf. A036537, A372328.
Similar sequences: A053143, A053149, A053167, A066638, A087320, A087321, A197863, A356191, A356192, A356193, A356194.
Differs from A102631 at n = 8, 24, 27, 32, 40, 54, 56, 64, ... .

f[p_, e_] := p^(2^Ceiling[Log2[e + 1]] - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

s(n) = {my(e=logint(n + 1, 2)); if(n + 1 == 2^e, n, 2^(e+1) - 1)};
a(n) = {my(f=factor(n)); prod(i=1, #f~, f[i, 1]^s(f[i, 2]))};

Multiplicative with a(p^e) = p^(2^ceiling(log_2(e+1)) - 1).
a(n) = n * A372328(n).
a(n) = n if and only if n is in A036537.
a(n) <= n^2, with equality if and only if n = 1.

A272245 Cubes of the form prime(n)+n.

Original entry on oeis.org

8, 27, 1000, 2744, 4096, 46656, 68921, 274625, 941192, 1295029, 1481544, 1906624, 14886936, 34328125, 35937000, 45882712, 50243409, 63521199, 64000000, 67917312, 76225024, 95443993, 112678587, 142236648, 143877824, 174676879, 198155287, 203297472, 216000000

Offset: 1

Emre APARI, Apr 23 2016

nonn

The cube root of the first 10 terms are: 2,3,10,14,16,36,41,65,98,109.

			prime(147) + 147 = 853 + 147 = 1000; which is 10^3.

Giovanni Resta, Table of n, a(n) for n = 1..500

Cf. A000578, A014688, A030078, A076147, A053149.

lista(nn) = {for (n=1, nn, if (ispower(p=n+prime(n), 3), print1(p, ", ")););} \\ Michel Marcus, Apr 23 2016

a(n) = A014688(A076147(n)). - Michel Marcus, Apr 23 2016

a(20)-a(29) from Giovanni Resta, Apr 23 2016

cp's OEIS Frontend

A372329 a(n) is the smallest multiple of n whose number of divisors is a power of 2 (A036537).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula