

A276935


Number of distinct prime factors prime(k) of n such that prime(k)^k, but not prime(k)^(k+1) is a divisor of n.


3



0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0
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OFFSET

1,18


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


FORMULA

a(1) = 0, for n > 1, a(n) = a(A028234(n)) + [A067029(n) = A055396(n)], where [] is Iverson bracket, giving 1 as its result when the stated equivalence is true and 0 otherwise.


EXAMPLE

For n = 12 = 2*2*3 = prime(1)^2 * prime(2)^1, neither of the prime factors satisfies the condition, thus a(12) = 0.
For n = 18 = 2*3*3 = prime(1)^1 * prime(2)^2, both prime factors satisfy the condition, thus a(18) = 1+1 = 2.
For n = 750 = 2*3*5*5*5 = prime(1)^1 * prime(2)^1 * prime(3)^3, only the prime factors 2 and 5 satisfy the condition, thus a(750) = 1+1 = 2.


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(definec (A276935 n) (if (= 1 n) 0 (+ (A276935 (A028234 n)) (if (= (A067029 n) (A055396 n)) 1 0))))


CROSSREFS

Cf. A276077, A276936.
Sequence in context: A219488 A129251 A276077 * A235127 A258059 A093956
Adjacent sequences: A276932 A276933 A276934 * A276936 A276937 A276938


KEYWORD

nonn


AUTHOR

Antti Karttunen, Sep 24 2016


STATUS

approved



