A057661 -id:A057661 - cp's OEIS frontend

A338647 a(n) = Sum_{k=1..n} 2^(k/gcd(n,k) - 1).

1, 2, 4, 7, 16, 22, 64, 92, 223, 342, 1024, 1132, 4096, 5462, 13534, 21937, 65536, 70978, 262144, 333472, 890590, 1398102, 4194304, 4528402, 16236031, 22369622, 57522106, 88435312, 268435456, 272976502, 1073741824, 1431677702, 3679303390, 5726623062, 16490405374, 18543422953

Offset: 1

Ilya Gutkovskiy, Apr 22 2021

nonn

Cf. A011782, A034738, A054432, A057661, A130586.

Table[Sum[2^(k/GCD[n, k] - 1), {k, 1, n}], {n, 1, 36}]

a(n) = sum(k=1, n, 2^(k/gcd(n,k) - 1)); \\ Michel Marcus, Apr 22 2021

a(n) = Sum_{d|n} A054432(d).

A357210 a(n) = Sum_{k=1..n} prime(k/gcd(n,k)).

Original entry on oeis.org

2, 4, 7, 11, 19, 22, 43, 46, 66, 68, 131, 90, 199, 158, 187, 223, 383, 242, 503, 320, 441, 478, 793, 436, 824, 716, 879, 734, 1373, 658, 1595, 1118, 1313, 1358, 1579, 1103, 2429, 1776, 1957, 1556, 3089, 1532, 3449, 2192, 2347, 2784, 4229, 2144, 4134, 2882, 3687, 3258, 5591

Offset: 1

Ilya Gutkovskiy, Sep 19 2022

nonn

Inverse Moebius transform of A127413.

Cf. A000040, A057661, A127413, A130029, A333558.

Table[Sum[Prime[k/GCD[n, k]], {k, 1, n}], {n, 1, 53}]

a(n) = sum(k=1, n, prime(k/gcd(n,k))); \\ Michel Marcus, Sep 20 2022

a(n) = Sum_{d|n} A127413(d).

cp's OEIS Frontend

A338647 a(n) = Sum_{k=1..n} 2^(k/gcd(n,k) - 1).

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