A359429 - OEIS

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A359429

a(n) = 1 if n is cubefree, but not squarefree, otherwise 0.

0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..100000` `Index entries for characteristic functions.` `Index entries for sequences computed from exponents in factorization of n.`
	FORMULA	`a(n) = A107078(n) * A212793(n) = A212793(n) - A008966(n).` `a(n) = [A072411(n) == 2] = [A290107(n) == 2], where [ ] is the Iverson bracket.` `a(n) >= A359474(n).` `Sum_{k=1..n} a(k) ~ c * n, where c = 1/zeta(3) - 1/zeta(2) = A088453 - A059956 = 0.22398... . - Amiram Eldar, Jan 05 2023`
	MATHEMATICA	`a[n_] := If[Max[FactorInteger[n][[;; , 2]]] == 2, 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)`
	PROG	`(PARI)` `A212793(n) = {f = factor(n); for (i=1, #f~, if ((f[i, 2]) >=3, return(0)); ); return (1); }; \\ From A212793.` `A359429(n) = (A212793(n)-issquarefree(n));`
	CROSSREFS	`Characteristic function of A067259.` `Cf. A008966, A072411, A107078, A212793, A290107, A359474.` `Cf. A059956, A088453.` `Sequence in context: A284954 A221151 A359474 * A353470 A342753 A358752` `Adjacent sequences: A359426 A359427 A359428 * A359430 A359431 A359432`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jan 04 2023`
	STATUS	`approved`

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Last modified August 18 23:41 EDT 2024. Contains 375284 sequences. (Running on oeis4.)