A178595 Natural numbers sorted by the sum of square roots of prime factors.

1, 2, 3, 5, 7, 4, 6, 11, 9, 13, 10, 15, 14, 17, 8, 19, 21, 25, 12, 22, 23, 18, 35, 26, 33, 20, 27, 49, 39, 30, 29, 28, 34, 55, 31, 16, 45, 38, 42, 65, 51, 50, 77, 24, 37, 57, 63, 44, 75, 46, 91, 36, 70, 85, 41, 52, 66, 40, 69, 43, 95, 54, 105, 121, 98, 125, 78, 119, 99, 60, 58

Offset: 1

Author

Joonas Pohjonen, May 30 2010

Keywords

• nonn

Comments

Prime factors counted with multiplicity. - Harvey P. Dale, May 20 2023

Links

• J. Pohjonen, Table of n, a(n) for n=1..1000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A001222, A027746.

Similarly defined sequences: A064364, A168521.

Programs

Mathematica

SortBy[Table[{n,Total[N[Sqrt[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]]]},{n,150}],Last][[;;,1]] (* Harvey P. Dale, May 20 2023 *)

Formula

For n >= 1, Sum_{k=1..A001222(a(n))} sqrt(A027746(a(n),k)) < Sum_{k=1..A001222(a(n+1))} sqrt(A027746(a(n+1),k)). - Peter Munn, Aug 17 2022