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A262900
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a(n) = number of leaf-children n has in the tree generated by edge-relation A049820(child) = parent.
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3
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0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0
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OFFSET
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0,23
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COMMENTS
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a(n) = number of such terms k in A045765 for which k - d(k) = n [where d(k) is the number of divisors of k, A000005(k)].
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LINKS
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FORMULA
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In the above formula [ ] stands for Iverson bracket, giving in the first instance as its result 1 only when A049820(k) = n (that is, when k is really a child of n), and 0 otherwise, and in the second instance 1 only when A060990(k) = 0 (that is, when k itself has no children), and 0 otherwise. - Comment corrected by Antti Karttunen, Nov 27 2015
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EXAMPLE
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a(4) = 1, as there is only one such term k in A045765 which satisfies the condition A049820(k) = 4, namely 8 (8 - d(8) = 4).
a(5) = 1, as the only term in A045765 satisfying the condition is 7, as 7 - d(7) = 5.
a(22) = 2, as there are exactly two terms in A045765 satisfying the condition, namely 25 and 28, as 25 - d(25) = 28 - d(28) = 22.
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PROG
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(Scheme)
(define (A262900 n) (let loop ((s 0) (k (A262686 n))) (cond ((<= k n) s) ((= n (A049820 k)) (loop (+ s (if (zero? (A060990 k)) 1 0)) (- k 1))) (else (loop s (- k 1))))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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