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

1,2

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

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

Mathematica

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

Crossrefs

Cf. A001222, A027746.

Similarly defined sequences: A064364, A168521.

Sequence in context: A239694 A097883 A290020 * A098284 A082196 A292876

Adjacent sequences: A178592 A178593 A178594 * A178596 A178597 A178598

Keyword

nonn

Author

Joonas Pohjonen, May 30 2010

Status

approved