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 A328246 Numbers whose third arithmetic derivative (A099306) is a squarefree number (A005117). 6
 9, 14, 18, 21, 25, 33, 38, 46, 49, 57, 65, 77, 85, 93, 98, 121, 126, 129, 134, 138, 141, 145, 150, 161, 166, 177, 185, 186, 194, 201, 205, 206, 209, 217, 221, 237, 242, 249, 253, 258, 262, 265, 266, 289, 290, 301, 305, 306, 315, 322, 326, 333, 334, 338, 341, 342, 350, 361, 365, 369, 375, 377, 381, 393, 398, 402, 413, 414 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n for which A008966(A003415(A003415(A003415(n)))) = 1. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 EXAMPLE For n=9, its first arithmetic derivative is A003415(9) = 6, its second derivative is A003415(6) = 5, and its third derivative is A003415(5) = 1, and 1 is a squarefree number (in A005117), thus 9 is included in this sequence. For n=14, A003415(14) = 9, A003415(9) = 6, A003415(6) = 5, and 5, like all primes, is a squarefree number, thus 14 is included in this sequence. For n=49, A003415(49) = 14, A003415(14) = 9, A003415(9) = 6 = 2*3, and 6 is a squarefree number, thus 49 is included in this sequence. PROG (PARI) A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); isA328246(n) = { my(u=A003415(A003415(A003415(n)))); (u>0 && issquarefree(u)); }; CROSSREFS Cf. A003415, A005117, A008966, A099306, A328234, A328244, A328245. Cf. A192192, A328239, A328247 (subsequences). Sequence in context: A011767 A305092 A205690 * A244466 A171123 A327896 Adjacent sequences: A328243 A328244 A328245 * A328247 A328248 A328249 KEYWORD nonn AUTHOR Antti Karttunen, Oct 11 2019 STATUS approved

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Last modified February 28 22:27 EST 2024. Contains 370400 sequences. (Running on oeis4.)