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A295662 Number of odd exponents larger than one in the canonical prime factorization of n. 9
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, 1, 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, 1, 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) = 0, a(p^e) = A000035(e) if e > 1.

a(1) = 0; and for n > 1, if A067029(n) = 1, a(n) = a(A028234(n)), otherwise A000035(A067029(n)) + a(A028234(n)).

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

a(n) <= A295659(n).

a(n) = 0 iff A295663(n) = 0, and when A295663(n) > 0, a(n) <= A295663(n).

EXAMPLE

For n = 24 = 2^3 * 3^1 there are two odd exponents, but only the other is larger than 1, thus a(24) = 1.

For n = 216 = 2^3 * 3^3 there are two odd exponents larger than 1, thus a(216) = 2.

MATHEMATICA

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

PROG

(Scheme, with memoization-macro definec)

(definec (A295662 n) (if (= 1 n) 0 (+ (if (= 1 (A067029 n)) 0 (A000035 (A067029 n))) (A295662 (A028234 n)))))

CROSSREFS

Cf. A056169, A162642, A295659, A295663, A295664.

Cf. A295661 (positions of nonzero terms).

Sequence in context: A277153 A323162 A295883 * A187946 A323510 A044938

Adjacent sequences:  A295659 A295660 A295661 * A295663 A295664 A295665

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 28 2017

STATUS

approved

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)