A244053 Let m = A244052(n) = n-th highly regular number; a(n) = number of numbers r <= m, all of whose prime divisors p also divide m.
1, 2, 3, 5, 6, 8, 10, 11, 18, 19, 26, 28, 32, 36, 41, 44, 68, 77, 80, 96, 115, 131, 145, 156, 166, 174, 183, 192, 283, 295, 313, 322, 382, 395, 452, 463, 505, 519, 551, 567, 593, 629, 660, 691, 717, 743, 766, 1161, 1224, 1253, 1257, 1285, 1306, 1526
Offset: 1
Keywords
Examples
a(5) = 6 since 6 is the fifth record value of A010846. The first record value is 1 set at position 1; the second is 2 set at position 2, the third is 3 set at position 4, the fourth is 5 set at position 6. Sequence A244052 records the positions of these record values.
Links
- Michael De Vlieger and David A. Corneth, Table of n, a(n) for n = 1..563 (terms 55-149 from David A. Corneth)
- Michael De Vlieger, Multiplicities of primes in the prime decomposition of A244052 and values of A244053.
Programs
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Mathematica
a010846[n_] := Block[{pf, a}, a[x_] := First /@ FactorInteger@ x; pf = a@ n; If[n == 1, 1, 1 + Count[Range@ n, ?(SubsetQ[pf, a@ #] &)]]]; f[n] := Block[{t = {}, max = 0, x}, Do[If[(x = a010846@ i) > max, max = x; AppendTo[t, a010846[i]]], {i, n}]; t]; f@ 1000 (* Michael De Vlieger, Feb 10 2015 *) Union@ Rest@ FoldList[Max, 0, Array[Count[Range@ #, k_ /; PowerMod[#, Floor@ Log2@ #, k] == 0] &, 10^3]] (* simplest, or *) f[n_] := If[n == 1, 1, Length@ Function[w, ToExpression@ StringJoin["Module[{n = ", ToString@ n, ", k = 0}, Flatten@ Table[k++, ", Most@ Flatten@ Map[{#, ", "} &, #], "]]"] &@ MapIndexed[Function[p, StringJoin["{", ToString@ Last@ p, ", 0, Log[", ToString@ First@ p, ", n/(", ToString@ InputForm[Times @@ Map[Power @@ # &, Take[w, First@ #2 - 1]]], ")]}"]]@ w[[First@ #2]] &, w]]@ Map[{#, ToExpression["p" <> ToString@ PrimePi@ #]} &, FactorInteger[n][[All, 1]]]]; Union@ Rest@ FoldList[Max, 0, Array[f, 10^4]] (* Michael De Vlieger, Mar 08 2017, more efficient *)
Comments