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A263077 a(n) = greatest k where A155043(k) < A155043(n).

%I A263077 #15 Oct 24 2015 12:21:41
%S A263077 0,0,2,2,6,2,12,6,6,6,12,6,18,12,18,18,22,12,30,18,30,18,34,22,22,22,
%T A263077 42,22,48,22,60,30,60,30,72,48,84,34,84,34,96,34,108,42,96,42,108,42,
%U A263077 48,48,120,48,132,48,132,48,140,60,140,48,140,72,140,140,140,72,140,84,140,84,140,60,140,96,140,96,150,96,156,96,108,108,120,72,120,120,132,108,140,108,140,132,140,120,140,84
%N A263077 a(n) = greatest k where A155043(k) < A155043(n).
%H A263077 Antti Karttunen, <a href="/A263077/b263077.txt">Table of n, a(n) for n = 1..124340</a>
%F A263077 a(n) = A263082(A155043(n)-1).
%t A263077 a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; Table[k = 3 n;
%t A263077 While[a@ k >= a@ n, k--]; k, {n, 96}] (* _Michael De Vlieger_, Oct 13 2015 *)
%o A263077 (PARI)
%o A263077 allocatemem((2^31)+(2^30));
%o A263077 uplim1 = 36756720 + 640; \\ = A002182(53) + A002183(53).
%o A263077 uplim2 = 36756720; \\ = A002182(53).
%o A263077 uplim3 = 32432400; \\ = A002182(52). Really just some Ad Hoc value smaller than above.
%o A263077 v155043 = vector(uplim1);
%o A263077 vother = vector(uplim3); \\ Contains A262503 and A263082 in succession.
%o A263077 v155043[1] = 1; v155043[2] = 1;
%o A263077 for(i=3, uplim1, v155043[i] = 1 + v155043[i-numdiv(i)]; if(!(i%1048576),print1(i,", ")));
%o A263077 A155043 = n -> if(!n,n,v155043[n]);
%o A263077 maxlen = 0; for(i=1, uplim2, len = v155043[i]; vother[len] = i; maxlen = max(maxlen,len); if(!(i%1048576),print1(i,", "))); \\ First it will be A262503.
%o A263077 print("uplim2=", uplim2, " uplim3=", uplim3, " maxlen=", maxlen);
%o A263077 \\ Then we convert it to A263082:
%o A263077 m = 0; for(i=1, maxlen, m = max(m, vother[i]); vother[i] = m; if(!(i%1048576),print1(i,", ")));
%o A263077 A263082 = n -> if(!n,n,vother[n]);
%o A263077 A263077 = n -> A263082(A155043(n)-1);
%o A263077 \\ Finally we can compute A263077:
%o A263077 for(i=1, uplim3, write("b263077.txt", i, " ", A263077(i)); );
%Y A263077 Cf. A155043, A261089, A262503, A263078, A263079, A263080, A263082.
%K A263077 nonn
%O A263077 1,3
%A A263077 _Antti Karttunen_, Oct 09 2015