A374352 a(n) = [n>1] * a(n-1) + Sum_{d|n} phi(lcm(d,n/d)) where [] is an Iverson bracket.

1, 3, 7, 12, 20, 28, 40, 52, 66, 82, 102, 122, 146, 170, 202, 228, 260, 288, 324, 364, 412, 452, 496, 544, 588, 636, 684, 744, 800, 864, 924, 980, 1060, 1124, 1220, 1290, 1362, 1434, 1530, 1626, 1706, 1802, 1886, 1986, 2098, 2186, 2278, 2382, 2472, 2560, 2688

Offset: 1

Author

Alois P. Heinz, Jul 05 2024

Keywords

• nonn

Comments

Sum over all positive integers k, m with k*m <= n of phi(lcm(k,m)).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Wikipedia, Iverson bracket

Crossrefs

Partial sums of A061884.

Cf. A000010, A003990, A051173, A372866.

Programs

Maple

a:= proc(n) option remember; uses numtheory; `if`(n<1, 0,
      a(n-1)+add(phi(ilcm(d, n/d)), d=divisors(n)))
    end:
seq(a(n), n=1..66);

Formula

a(n) = Sum_{j=1..n} Sum_{d|j} phi(lcm(d,j/d)).

a(n) = Sum_{j=1..n} A061884(j).