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A086956
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a(1)=1, for n>1: a(n) = smallest divisor of n occurring earlier at most twice.
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9
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1, 1, 1, 2, 5, 2, 7, 2, 3, 5, 11, 3, 13, 7, 3, 4, 17, 6, 19, 4, 7, 11, 23, 4, 5, 13, 9, 14, 29, 6, 31, 8, 11, 17, 35, 6, 37, 19, 13, 8, 41, 14, 43, 22, 9, 23, 47, 8, 49, 10, 17, 26, 53, 9, 55, 14, 19, 29, 59, 10, 61, 31, 21, 16, 65, 22, 67, 34, 23, 10, 71, 12, 73, 37, 15, 38
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| For all natural numbers m exist exactly three numbers u(m)<v(m)<w(m) with m=a(u(m))=a(v(m))=a(w(m)) (see A086957=u, A086958=v, A086959=w),
permuting {u,v,w} induces 6=3! permutations of natural numbers: [(2,3,1)]->A086960, [(3,2,1)]->A086961, [(1)(2,3)]->A086962, [(2)(3,1)]->A086963, [(3)(2,1)]->A086964 and [(1,2,3)]->A000027.
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LINKS
| Eric Weisstein's World of Mathematics, Divisor
Eric Weisstein's World of Mathematics, Permutation.
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EXAMPLE
| a(p) = p for primes p>3;
divisor set of n=20: {1,2,4,5,10,20}, divisors occurring <20:
1=a(1)=a(2)=a(3), 2=a(4)=a(6)=a(8), 4=a(16); as 4 occurs only once a(20)=4.
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CROSSREFS
| Cf. A086571, A086572.
Sequence in context: A067948 A142148 A142583 * A198570 A190290 A016580
Adjacent sequences: A086953 A086954 A086955 * A086957 A086958 A086959
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 25 2003
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