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 A178595 Natural numbers sorted by the sum of square roots of prime factors. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 4 20:53 EDT 2023. Contains 365888 sequences. (Running on oeis4.)