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A295883 Number of exponents that are 3 in the prime factorization of n. 5
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,216

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

FORMULA

Additive with a(p^3) = 1, a(p^e) = 0 when e <> 3.

a(n) = A295659(n) - A295884(n).

a(n) <= A295662(n) <= A295663(n).

EXAMPLE

For n = 8 = 2^3, there is one exponent that is exactly 3, thus a(8) = 1.

For n = 216 = 2^3 * 3^3 there are two exponents that are exactly 3, thus a(216) = 2.

For n = 432 = 2^4 * 3^3, there is one exponent that is exactly 3, thus a(432) = 1.

MATHEMATICA

Array[Total@ Map[Boole[# == 3] &, FactorInteger[#][[All, -1]]] &, 120] (* Michael De Vlieger, Nov 29 2017 *)

Count[FactorInteger[#][[All, 2]], 3]&/@Range[120] (* Harvey P. Dale, Apr 13 2019 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A295883 n) (if (= 1 n) 0 (+ (if (= 3 (A067029 n)) 1 0) (A295883 (A028234 n)))))

CROSSREFS

Cf. A295659, A295662, A295663, A295884.

Sequence in context: A276404 A277153 A323162 * A295662 A187946 A330549

Adjacent sequences:  A295880 A295881 A295882 * A295884 A295885 A295886

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 29 2017

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)