A340363 - OEIS

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A340363

a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime and i, j >= 0, otherwise 0.

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

	OFFSET	`1`
	COMMENTS	`a(n) = 1 if the odd part of n has no more than one distinct prime divisor, and 0 otherwise.`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..65537` `Index entries for characteristic functions`
	FORMULA	`a(n) = A010055(A000265(n)).` `a(n) = [A005087(n) <= 1], where [ ] is the Iverson bracket, and A005087(n) = A001221(A000265(n)).` `a(n) = A209229(n) + A340373(n).` `For all n, a(n) <= A340372(n).`
	PROG	`(PARI)` `A000265(n) = (n>>valuation(n, 2));` `A340363(n) = (omega(A000265(n))<=1);`
	CROSSREFS	`Cf. A000265, A001221, A005087, A010055, A209229, A340372, A340373.` `Characteristic function of {1} U A070776.` `Sequence in context: A133011 A296079 A354806 * A340372 A167850 A167851` `Adjacent sequences: A340360 A340361 A340362 * A340364 A340365 A340366`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jan 06 2021`
	STATUS	`approved`

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Last modified March 20 09:21 EDT 2023. Contains 361366 sequences. (Running on oeis4.)