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A147763 a(n) = smallest k such that n = d*(d-b)*(d+c), where b, c, d >= 0 and k = b+c.

%I A147763 #12 Sep 08 2022 08:45:38
%S A147763 0,1,2,1,4,2,6,0,2,4,10,1,12,6,4,2,16,1,18,3,6,10,22,2,4,12,0,5,28,3,
%T A147763 30,2,10,16,6,1,36,18,12,3,40,5,42,9,2,22,46,1,6,3,16,11,52,3,10,5,18,
%U A147763 28,58,2,60,30,4,0,12,9,66,15,22,5,70,3,72,36,2,17,10,11,78,1,6,40,82,4,16
%N A147763 a(n) = smallest k such that n = d*(d-b)*(d+c), where b, c, d >= 0 and k = b+c.
%H A147763 David A. Corneth, <a href="/A147763/b147763.txt">Table of n, a(n) for n = 1..10000</a>
%F A147763 a(n) = n-1 for n prime; a(n) = 0 for n a 3rd power. - _Klaus Brockhaus_, Nov 19 2008
%e A147763 n = 9 = 3*1*3 = 3*(3-2)*(3+0) with d = 3, b = 2, c = 0. So a(9) = k = 2+0 = 2, since there is no solution with k = 1.
%o A147763 (Magma) [ Min(v) where v is [ b+c: d, y, z in Divisors(n) | d*(d-b)*(d+c) eq n and d ge 0 and b ge 0 and c ge 0 where b is d-y where c is z-d ]: n in [1..85] ]; // _Klaus Brockhaus_, Nov 19 2008
%o A147763 (PARI) first(n) = {my(res = vector(n, i, i), t = 0); for(i = 1, n, for(j = i, n \ i, for(k = j, n \ (i * j), res[i * j * k] = min(res[i * j * k], k - i)))); res} \\ _David A. Corneth_, May 12 2018
%Y A147763 Cf. A056737.
%K A147763 nonn,easy
%O A147763 1,3
%A A147763 Samuel Zbarsky (sa_zbarsky(AT)yahoo.com), Nov 11 2008
%E A147763 Definition and example edited, and extended beyond a(42) by _Klaus Brockhaus_, Nov 19 2008