

A266116


The last nonzero term on each row of A265751.


4



7, 7, 13, 7, 8, 7, 13, 7, 8, 13, 20, 13, 25, 13, 20, 19, 24, 19, 25, 19, 20, 37, 25, 37, 24, 25, 40, 37, 28, 37, 50, 37, 40, 33, 50, 37, 36, 37, 50, 43, 40, 43, 49, 43, 50, 67, 49, 67, 56, 49, 50, 67, 52, 67, 68, 55, 56, 67, 68, 67, 136, 67, 68, 63, 64, 67, 66, 67, 68, 79, 74, 79, 136, 79, 74, 75, 103, 79, 98, 79, 88, 103, 98, 103, 136, 85
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OFFSET

0,1


COMMENTS

Starting from j = n, search for a smallest number k such that k  d(k) = j, and if found such a number, replace j with k and repeat the procedure. When eventually such k is no longer found, then the (last such) j must be one of the terms of A045765, and it is set as the value of a(n).


LINKS



FORMULA

If A060990(n) = 0, a(n) = n, otherwise a(n) = a(A082284(n)), where A082284(n) = smallest number k such that k  d(k) = n, or 0 if no such number exists, and d(n) = the number of divisors of n (A000005).
Other identities and observations. For all n >= 0:
a(n) >= n.


EXAMPLE

Starting from n = 21, we get the following chain: 21 > 23 > 27 > 29 > 31 > 35 > 37, with A082284 iterated 6 times before the final term 37 (for which A060990(37) = A082284(37) = 0) is encountered. Thus a(21) = 37.


PROG

(Scheme)
;; Alternatively:


CROSSREFS

Cf. A266110 (gives the number of iterations of A082284 needed before a(n) is found).
Cf. also tree A263267 (and its illustration).


KEYWORD

nonn


AUTHOR



STATUS

approved



