This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A276332 #7 Aug 31 2016 20:55:55 %S A276332 0,1,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,1,2,5,6,7,8,6,7,8,9,7,8,9,10,8,9, %T A276332 10,11,2,3,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,3,4,7,8,9,10,8,9,10,11,9, %U A276332 10,11,12,10,11,12,13,4,5,6,7,5,6,7,8,6,7,8,9,7,8,9,10,8,9,5,6,9,10,11,12,1 %N A276332 a(n) = number of terms of A001563 needed to sum to n when always choosing the largest term that divides the remaining n, a(0) = 0. %H A276332 Antti Karttunen, <a href="/A276332/b276332.txt">Table of n, a(n) for n = 0..4320</a> %F A276332 a(0) = 0; for n >= 1, a(n) = 1 + a(n-A276330(n)) = 1 + a(A276331(n)). %F A276332 Other identities and observations: %F A276332 It seems that a(n) >= A276328(n) for all n. %e A276332 For n=20, the largest term of A001563 that divides 20 is 4 and moreover, 4 is also the largest term of A001563 that divides 16, 12, 8 and 4, thus as 20 = 5*4, a(20) = 5. %e A276332 For n=21, the largest term of A001563 that divides 21 is A001563(1) = 1, and case for 21 - 1 = 20 is shown above, thus a(21) = 1 + 5 = 6. %o A276332 (Scheme, with memoization-macro definec) %o A276332 (definec (A276332 n) (if (zero? n) n (+ 1 (A276332 (A276331 n))))) %Y A276332 Cf. A001563, A276328, A276329, A276330, A276331. %K A276332 nonn %O A276332 0,3 %A A276332 _Antti Karttunen_, Aug 30 2016