A110663 Triangle read by rows: T(n,k) = Sum_{j=k..n} phi(j) (1<=k<=n), where phi is Euler's totient function.

1, 2, 1, 4, 3, 2, 6, 5, 4, 2, 10, 9, 8, 6, 4, 12, 11, 10, 8, 6, 2, 18, 17, 16, 14, 12, 8, 6, 22, 21, 20, 18, 16, 12, 10, 4, 28, 27, 26, 24, 22, 18, 16, 10, 6, 32, 31, 30, 28, 26, 22, 20, 14, 10, 4, 42, 41, 40, 38, 36, 32, 30, 24, 20, 14, 10, 46, 45, 44, 42, 40, 36, 34, 28, 24, 18, 14, 4

Offset

1,2

Links

Indranil Ghosh, Rows 1..100, flattened

Formula

T(n,n) = phi(n) = A000010(n) = number of numbers <=n and relatively prime to n.

T(n,1) = Sum_{j=1..n} phi(j) = A002088(n).

Example

T(5,3) = 8 because phi(3)+phi(4)+phi(5) = 2+2+4 = 8.
Triangle begins:
1;
2,1;
4,3,2;
6,5,4,2;
10,9,8,6,4;
...

Mathematica

T[n_, n_] := EulerPhi[n]; T[n_, k_] := Sum[EulerPhi[j], {j, k, n}];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Sep 03 2017 *)

Prog

(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(sum(j=k, n, eulerphi(j)), ", "); ); print(); ); } \\ Michel Marcus, Apr 05 2015

Crossrefs

Cf. A000010, A002088.

Sequence in context: A082494 A194187 A174375 * A294317 A064277 A287010

Adjacent sequences: A110660 A110661 A110662 * A110664 A110665 A110666

Keyword

nonn,tabl

Author

Emeric Deutsch, Aug 02 2005

Status

approved