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 A285319 Squarefree numbers n for which A019565(n) < n and A048675(n) is also squarefree. 9
 66, 129, 130, 258, 514, 1034, 1041, 1042, 2049, 2054, 2055, 2066, 2082, 2114, 4098, 4101, 4102, 4130, 4161, 4162, 4226, 4353, 4354, 4610, 5122, 8193, 8198, 8202, 8205, 8206, 8210, 8211, 8229, 8259, 8706, 9218, 9219, 12291 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Any finite cycle in A019565, if such cycles exist at all, must have at least one member that occurs somewhere in this sequence. Furthermore, such a number n should satisfy A019565(n) < n and that A048675(n)^k is squarefree for all k >= 0. LINKS Table of n, a(n) for n=1..38. MATHEMATICA lim = 4000; A019565 = Table[Times @@ Prime@Flatten@Position[#, 1] &@ Reverse@IntegerDigits[n, 2], {n, 1, lim}]; (* From Michael De Vlieger in A019565 *) A048675 = Table[Total[#[[2]]*2^(PrimePi[#[[1]]] - 1) & /@ FactorInteger[n]], {n, 1, lim}]; (* From Jean-François Alcover in A048675 *) Select[Range[lim], A019565[[#]] < # && SquareFreeQ[#] && SquareFreeQ[A048675[[#]]] &] (* Robert Price, Apr 07 2019 *) PROG (PARI) allocatemem(2^30); A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016 isA285319(n) = (issquarefree(n) & (A019565(n) < n) && issquarefree(A048675(n))); n=0; k=0; while(k <= 60, n=n+1; if(isA285319(n), print1(n, ", "); k=k+1)); (Scheme, with Antti Karttunen's IntSeq-library) (define A285319 (MATCHING-POS 1 0 (lambda (n) (and (< (A019565 n) n) (not (zero? (A008683 n))) (not (zero? (A008683 (A048675 n)))))))) CROSSREFS Subsequence of A285317. Cf. A008683, A019565, A048675. Cf. also A285320 and discussion in A285331 and A285332. Sequence in context: A350204 A031184 A039443 * A044189 A044570 A118163 Adjacent sequences: A285316 A285317 A285318 * A285320 A285321 A285322 KEYWORD nonn,hard,more AUTHOR Antti Karttunen, Apr 18 2017 STATUS approved

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Last modified February 27 04:33 EST 2024. Contains 370362 sequences. (Running on oeis4.)