A378182 Sum of row n of A378180.

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 25, 1, 10, 9, 15, 1, 25, 1, 47, 11, 14, 1, 90, 6, 16, 13, 77, 1, 80, 1, 31, 15, 20, 13, 90, 1, 22, 17, 250, 1, 116, 1, 161, 58, 26, 1, 301, 8, 47, 21, 215, 1, 90, 17, 554, 23, 32, 1, 490, 1, 34, 90, 63, 19, 212, 1, 347, 27, 152

Offset: 1

Author

Michael De Vlieger, Nov 20 2024

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A007947, A024619, A244974, A376567, A377071, A378180.

Programs

Mathematica

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
Block[{k}, Table[k = PrimeOmega[n];
  Total@ Select[Range[n^PrimeNu[n]],
    Divisible[n, rad[#]] && PrimeOmega[#] < k &], {n, 60}]]

Formula

a(n) = A376567(n) - A377071(n).

For prime p, a(p) = 1.

For prime power p^k, a(p^k) = A244974(p^k)-p^k = A000203(p^k)-p^k.

a(2^k) = 2^k - 1.

For n in A024619, a(n) != A244974(n).