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A359547
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Numbers such that they are not divisible by p^p for any prime p, but for some k-th arithmetic derivative (k >= 1) of n such a factor exists.
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5
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15, 26, 35, 39, 45, 50, 51, 55, 63, 69, 74, 75, 86, 87, 90, 91, 95, 99, 102, 106, 110, 111, 115, 117, 119, 122, 123, 125, 133, 134, 141, 143, 146, 147, 153, 155, 158, 159, 169, 171, 175, 178, 183, 187, 190, 194, 195, 198, 203, 207, 210, 213, 215, 218, 219, 225, 226, 230, 234, 235, 245, 247, 249, 250
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Michael De Vlieger, 4096 X 4096 pixel raster with origin (0, 0) in the upper left corner and black pixels at (x, y), indicate a number 4096*(y-1) + (x-1) in this sequence. Thus this image contains 7852685 terms of this sequence.
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EXAMPLE
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15 = 3*5 is present, as although it itself is not in A100716, its arithmetic derivative 15' = 8 is there.
26 = 2*13 is present, as although neither 26 nor 26' = 15 are in A100716, its second derivative = 26'' = 15' = 8 is there.
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MATHEMATICA
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f[n_] := f[n] = Which[Abs@ n < 2, 0, PrimeQ[n], 1, True, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]]; g[n_] := And[n > 0, AnyTrue[FactorInteger[n], #2 >= #1 & @@ # &]]; w = {}; nn = 2^16; k = 1; While[Set[m, #^#] <= nn &[Prime[k]], AppendTo[w, m]; k++]; Reap[Do[If[! g[n], If[g@ NestWhile[f, n, And[! Divisible[#, 4], FreeQ[w, #]] &], Sow[n] ] ], {n, 2, nn}] ][[-1, -1]]
(* or, generate up to 7852685 terms of this sequence from the bitmap by setting y to a number not exceeding 4096: *)
With[{img = https://oeis.org/A359547/a359547.png, y = 2}, Map[4096 (#1 - 1) + #2 - 1 & @@ # &, Position[ImageData[img][[1 ;; y, All]], 0.]] ] (* Michael De Vlieger, Jan 23 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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