A342485
a(n) = Sum_{d|n} phi(d)^(d+1).
Original entry on oeis.org
1, 2, 17, 34, 4097, 146, 1679617, 262178, 60466193, 4198402, 1000000000001, 67109042, 1283918464548865, 470186664194, 281474976714769, 2251799813947426, 4722366482869645213697, 609359800476818, 12748236216396078174437377, 9223372036858974242
Offset: 1
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a[n_] := DivisorSum[n, EulerPhi[#]^(#+1) &]; Array[a, 20] (* Amiram Eldar, Mar 14 2021 *)
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a(n) = sumdiv(n, d, eulerphi(d)^(d+1));
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a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n/gcd(k, n)));
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my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k+1)*x^k/(1-x^k)))
A342487
a(n) = Sum_{d|n} phi(d)^(n+1).
Original entry on oeis.org
1, 2, 17, 34, 4097, 258, 1679617, 262658, 60467201, 8388610, 1000000000001, 67133442, 1283918464548865, 940369969154, 281479271743489, 2251816993685506, 4722366482869645213697, 1218719481069570, 12748236216396078174437377, 9223380832949895170
Offset: 1
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a[n_] := DivisorSum[n, EulerPhi[#]^(n+1) &]; Array[a, 20] (* Amiram Eldar, Mar 14 2021 *)
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a(n) = sumdiv(n, d, eulerphi(d)^(n+1));
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a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^n);
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my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k+1)*x^k/(1-(eulerphi(k)*x)^k)))
A342543
a(n) = Sum_{k=1..n} phi(gcd(k, n))^gcd(k, n).
Original entry on oeis.org
1, 2, 10, 19, 1028, 76, 279942, 65558, 10077718, 1049608, 100000000010, 16777334, 106993205379084, 78364444044, 35184372090920, 281474976776236, 295147905179352825872, 101559966746268, 708235345355337676357650, 1152921504607897676, 46005119909369702026044, 10000000000100000000020
Offset: 1
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a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^# &]; 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));
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a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^d);
A342608
a(n) = Sum_{d|n} phi(d)^(n+d).
Original entry on oeis.org
1, 2, 65, 258, 1048577, 4610, 78364164097, 4294971394, 101559956672513, 1100585369602, 10000000000000000000001, 281474977071106, 11447545997288281555215581185, 6140964151415455875074, 1237940039285381374411014145, 79228162514264619068521709570
Offset: 1
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a[n_] := DivisorSum[n, EulerPhi[#]^(n + #) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *)
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a(n) = sumdiv(n, d, eulerphi(d)^(n+d));
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a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n+n/gcd(k, n)-1));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (eulerphi(k)^2*x)^k/(1-(eulerphi(k)*x)^k)))
Showing 1-4 of 4 results.