A342421 -id:A342421 - cp's OEIS frontend

A342436 a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 1).

1, 3, 11, 68, 629, 7791, 117655, 2097224, 43046745, 1000000637, 25937424611, 743008378618, 23298085122493, 793714773371811, 29192926025391919, 1152921504608944272, 48661191875666868497, 2185911559738739594277, 104127350297911241532859

Offset: 1

Seiichi Manyama, Mar 12 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..387

Cf. A000010, A056665, A342421, A342423, A342435.

a[n_] := Sum[GCD[k, n]^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 12 2021 *)

a(n) = sum(k=1, n, gcd(k, n)^(gcd(k, n)-1));

a(n) = sumdiv(n, d, eulerphi(n/d)*d^(d-1));

a(n) = Sum_{d|n} phi(n/d) * d^(d-1).

A342422 a(n) = Sum_{k=1..n} (n/gcd(k,n))^gcd(k,n).

Original entry on oeis.org

1, 3, 7, 13, 21, 39, 43, 81, 109, 173, 111, 475, 157, 507, 1107, 1153, 273, 2997, 343, 6133, 6685, 3479, 507, 30819, 13001, 10533, 44227, 65071, 813, 234959, 931, 215553, 368265, 136241, 414183, 1991281, 1333, 531471, 3215947, 4883141, 1641, 12951117, 1807, 12735043, 36892689, 8401259

Offset: 1

Seiichi Manyama, Mar 11 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Cf. A000010, A342421.

a[n_] := Sum[(n/GCD[k, n])^GCD[k, n], {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Mar 11 2021 *)

a(n) = sum(k=1, n, (n/gcd(k, n))^gcd(k, n));

a(n) = sumdiv(n, d, eulerphi(d^(n/d+1)));

a(n) = sumdiv(n, d, eulerphi(d)*d^(n/d));

a(n) = Sum_{d|n} phi(d^(n/d+1)) = Sum_{d|n} phi(d) * d^(n/d).

A342437 a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n) - 1).

Original entry on oeis.org

1, 2, 3, 5, 5, 14, 7, 25, 25, 74, 11, 161, 13, 398, 383, 657, 17, 2110, 19, 3341, 4485, 10262, 23, 19569, 2521, 49178, 39547, 74441, 29, 221462, 31, 328737, 590753, 1048610, 103379, 1905565, 37, 4718630, 6377655, 5573801, 41, 22462826, 43, 31459985, 40634221, 92274734, 47

Offset: 1

Seiichi Manyama, Mar 12 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Cf. A000010, A226459, A342421, A342424.

a[n_] := Sum[GCD[k, n]^(n/GCD[k, n] - 1), {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Mar 12 2021 *)

a(n) = sum(k=1, n, gcd(k, n)^(n/gcd(k, n)-1));

a(n) = sumdiv(n, d, eulerphi(n/d)*d^(n/d-1));

a(n) = Sum_{d|n} phi(n/d) * d^(n/d-1).

If p is prime, a(p) = p.

cp's OEIS Frontend

A342436 a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A342422 a(n) = Sum_{k=1..n} (n/gcd(k,n))^gcd(k,n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

PARI

Formula

A342437 a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n) - 1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula