A342544
a(n) = Sum_{k=1..n} phi(gcd(k, n))^(gcd(k, n) - 1).
Original entry on oeis.org
1, 2, 6, 11, 260, 40, 46662, 16398, 1679630, 262408, 10000000010, 4194366, 8916100448268, 13060740684, 4398046511640, 35184372105244, 18446744073709551632, 16926661124436, 39346408075296537575442, 144115188076118572, 3833759992447475215524, 1000000000010000000020
Offset: 1
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a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(# - 1) &]; Array[a, 20] (* Amiram Eldar, Mar 15 2021 *)
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a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(gcd(k, n)-1));
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a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^(d-1));
A342370
a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).
Original entry on oeis.org
1, 3, 11, 68, 629, 7797, 117655, 2097254, 43046979, 1000000799, 25937424611, 743008402000, 23298085122493, 793714773374529, 29192926027528343, 1152921504613147242, 48661191875666868497, 2185911559739107208115, 104127350297911241532859, 5242880000000008181608132
Offset: 1
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a[n_] := Sum[GCD[k, n]^(k - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)
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a(n) = sum(k=1, n, gcd(k, n)^(k-1));
A342435
a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 2).
Original entry on oeis.org
1, 2, 5, 19, 129, 1303, 16813, 262166, 4782981, 100000133, 2357947701, 61917365564, 1792160394049, 56693912392115, 1946195068359645, 72057594038190124, 2862423051509815809, 121439531096599037355
Offset: 1
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a[n_] := Sum[GCD[k, n]^(GCD[k, n] - 2), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 12 2021 *)
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a(n) = sum(k=1, n, gcd(k, n)^(gcd(k, n)-2));
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a(n) = sumdiv(n, d, eulerphi(n/d)*d^(d-2));
Showing 1-3 of 3 results.