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A360589 Numbers k that set records in A355432. 4
1, 18, 48, 54, 162, 384, 486, 1350, 1458, 2250, 2430, 3750, 6000, 6750, 7290, 11250, 12150, 14580, 15000, 15360, 18750, 21870, 30720, 33750, 36450, 37500, 43740, 56250, 61440, 65610, 93750, 122880, 168750 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Subset of A055932.
For n > 1, subset of A360768, which is in turn a subset of A126706.
LINKS
EXAMPLE
Let rad(m) = A007947(m).
a(1) = 1 since 1 is the empty product.
a(2) = 18 since {12} is a nondivisor k < 18 such that rad(k) = rad(18).
a(3) = 48 since {18, 36} are nondivisors k < 48 such that rad(k) = rad(48).
a(4) = 54 since {12, 24, 36, 48} are nondivisors k < 54 such that rad(k) = rad(54), etc.
Table shows prime decomposition of a(n) = Product p^e, noting multiplicity e in the pi(p)-th position. For example, a(n) = 1350 = 2 * 3^3 * 5^2, hence we write 1.3.2.
a(n) = A055932(i) and has A360912(n) nondivisors k < a(n) such that rad(k) = rad(a(n)).
n a(n) A067255(a(n)) i A360912(n)
----------------------------------------
1 1 0 1 0
2 18 1.2 8 1
3 48 4.1 13 2
4 54 1.3 14 4
5 162 1.4 25 8
6 384 7.1 37 10
7 486 1.5 42 14
8 1350 1.3.2 65 16
9 1458 1.6 67 21
10 2250 1.2.3 81 23
11 2430 1.5.1 85 26
12 3750 1.1.4 99 33
...
MATHEMATICA
rad[n_] := rad[n] = Times @@ FactorInteger[n][[All, 1]]; t = Select[Range[2^14], Nor[SquareFreeQ[#], PrimePowerQ[#]] &]; s = Select[t, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]; t = Table[m = s[[n]]; r = rad[m]; Count[TakeWhile[t, # < m &], _?(And[rad[#] == r, Mod[m, #] != 0] &)], {n, Length[s]}]; {1}~Join~Map[s[[FirstPosition[t, #][[1]]]] &, Union@ FoldList[Max, t]]
CROSSREFS
Sequence in context: A034132 A218630 A099119 * A105520 A067726 A234956
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Feb 22 2023
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)