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A301415 Number of terms m in A002110 such that A301413(k) * A002110(m) is in A002182. 2
3, 3, 3, 3, 3, 3, 4, 3, 3, 5, 3, 4, 4, 5, 5, 5, 4, 3, 4, 4, 4, 6, 3, 4, 5, 4, 3, 4, 3, 7, 5, 5, 6, 9, 6, 5, 8, 6, 8, 8, 8, 6, 6, 8, 6, 5, 7, 8, 9, 5, 5, 7, 6, 5, 6, 5, 6, 5, 6, 9, 9, 6, 9, 9, 6, 6, 7, 8, 7, 7, 7, 9, 5, 10, 10, 5, 13, 9, 9, 8, 10, 10, 7, 10, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers m = A301414(x) * A002110(y) that are in A002182 are plotted below. Those also in A002201 are followed by asterisk.
This sequence counts the terms in each column.
1 2 3 4 5 6 7 ...
+-----------------------------------------
0 | 1
1 | 2* 4
2 | 6* 12* 24 36 48
3 | 60* 120* 180 240 360* 720
4 | 840 1260 1680 2520* 5040*
5 | 27720 55440*
6 | 720720*
...
LINKS
Michael De Vlieger, Plot m = A301414(x) * A002110(y) at (x,y) for all 779674 m in Achim Flammenkamp's dataset SHCNs are shown in red; 8563 * 4096 pixels.
EXAMPLE
a(1) = 3 since A301414(1) = 1 produces 3 highly composite numbers when multiplied by primorials p_0#, p_1#, and p_2# = {1, 2, 6}.
a(2) = 3 since A301414(2) = 2 yields 3 HCNs, multiplied by p_1#, p_2#, and p_3# = {4, 12, 60}.
MATHEMATICA
f[n_] := With[{d = FactorInteger@ n}, If[n == 1, {0}, ReplacePart[Table[0, {PrimePi[d[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, d]]]; Take[#, 85] &@ Block[{s = a002182, a, b, c, m, u}, s = Take[s, 1000]; a = Array[{#2, #1, StringTrim[StringReplace[ToString@ #, ", " -> "."], ("{" | "}") ...] &[#3 /. {} -> 0], Times @@ MapIndexed[Prime[First@ #2]^#1 &, #3]} & @@ {#1, Boole[First@ #2 > 0] Length@ #2, DeleteCases[-1 + #2, 0] /. -1 -> 0} & @@ {s[[#]], f@ s[[#]]} &, Length@ s]; u = Union@ a[[All, -1]]; b = MapIndexed[{i_, j_, k_, #1} -> ToExpression@ StringJoin["{i, ", ToString@ First@ #2, ", ", " j, k}"] &, Union@ a[[All, -1]]]; c = Map[# /. b &, a]; m = Max[c[[All, 2]] ]; c = Map[Sort@ # &, SplitBy[SortBy[c, First], First]]; Total /@ Transpose@ Array[With[{t = ConstantArray[0, m]}, ReplacePart[t, Map[#2 -> 1 & @@ # &, c[[#]] ] ] ] &, Length@ c] ]
CROSSREFS
Sequence in context: A063438 A276870 A081168 * A210509 A362049 A333819
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Apr 09 2018
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)