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A249744 a(n) = 0 if n is 1 or a prime, otherwise, when n = A020639(n) * A032742(n), a(n) = the largest m < n such that A020639(m) = A020639(n), where A020639(n) and A032742(n) are the smallest prime and the largest proper divisor dividing n.

%I A249744 #21 Mar 08 2016 05:14:15
%S A249744 0,0,0,2,0,4,0,6,3,8,0,10,0,12,9,14,0,16,0,18,15,20,0,22,5,24,21,26,0,
%T A249744 28,0,30,27,32,25,34,0,36,33,38,0,40,0,42,39,44,0,46,7,48,45,50,0,52,
%U A249744 35,54,51,56,0,58,0,60,57,62,55,64,0,66,63,68,0,70,0,72,69,74,49,76,0,78,75,80,0,82,65,84,81,86,0,88,77,90,87,92,85,94,0,96,93,98,0,100
%N A249744 a(n) = 0 if n is 1 or a prime, otherwise, when n = A020639(n) * A032742(n), a(n) = the largest m < n such that A020639(m) = A020639(n), where A020639(n) and A032742(n) are the smallest prime and the largest proper divisor dividing n.
%C A249744 For all composite numbers, a(n) tells what is the previous number processed by the sieve of Eratosthenes, i.e., number which is immediately left of n on the same row where n is in arrays like A083140, A083221.
%H A249744 Antti Karttunen, <a href="/A249744/b249744.txt">Table of n, a(n) for n = 1..10000</a>
%F A249744 a(n) = A020639(n) * A249738(n).
%F A249744 Other identities. For all n >= 1 it holds:
%F A249744 a(2n) = 2n-2.
%F A249744 a(A001248(n)) = A000040(n). [I.e., a(p^2) = p for primes p.]
%t A249744 a[1] = 0; a[_?PrimeQ] = 0; a[n_] := For[p = FactorInteger[n][[1, 1]]; m = n - p, True, m = m - p, If[FactorInteger[m][[1, 1]] == p, Return[m]]]; Array[a, 102] (* _Jean-François Alcover_, Mar 08 2016 *)
%o A249744 (Scheme) (define (A249744 n) (* (A020639 n) (A249738 n)))
%Y A249744 Can be used to compute A078898.
%Y A249744 Cf. A000040, A001248, A020639, A083140, A083221, A249738, A250469, A250470.
%K A249744 nonn
%O A249744 1,4
%A A249744 _Antti Karttunen_, Dec 06 2014