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A295659 Number of exponents larger than 2 in the prime factorization of n. 9
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 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^e) = 1 if e>2, 0 otherwise.

a(n) = 0 iff A212793(n) = 1.

a(n) = A001221(A053150(n)).

a(n) = A056170(A003557(n)).

a(n) >= A295662(n) = A162642(n) - A056169(n).

a(n) = A295883(n) + A295884(n).

EXAMPLE

For n = 120 = 2^3 * 3^1 * 5^1 there is only one exponent larger than 2, thus a(120) = 1.

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

MATHEMATICA

Array[Count[FactorInteger[#][[All, -1]], _?(# > 2 &)] &, 105] (* Michael De Vlieger, Nov 28 2017 *)

PROG

(Scheme, with memoization-macro definec) (definec (A295659 n) (if (= 1 n) 0 (+ (if (> (A067029 n) 2) 1 0) (A295659 (A028234 n)))))

(PARI) a(n) = { my(v = factor(n)[, 2], i=0); for(x=1, length(v), if(v[x]>2, i++)); i; } \\ Iain Fox, Nov 29 2017

CROSSREFS

Cf. A001221, A003557, A053150, A056169, A056170, A162642, A295657, A295662, A295883, A295884.

Cf. A004709 (positions of zeros), A046099 (of nonzeros), A212793.

Sequence in context: A044938 A072401 A064873 * A188436 A037823 A293162

Adjacent sequences:  A295656 A295657 A295658 * A295660 A295661 A295662

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 28 2017

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)