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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Analogous to A002183.

Records transform of A010846. -Michael De Vlieger, Mar 08 2017

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.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A244052, A002183, A010846.

Sequence in context: A005243 A117045 A324793 * A275833 A307113 A025055

Adjacent sequences:  A244050 A244051 A244052 * A244054 A244055 A244056

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Jun 18 2014

STATUS

approved

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Last modified September 16 06:48 EDT 2019. Contains 327090 sequences. (Running on oeis4.)