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

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, 42, 22, 48, 22, 60, 30, 60, 30, 72, 48, 84, 34, 84, 34, 96, 34, 108, 42, 96, 42, 108, 42, 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

Offset: 1

Author

Antti Karttunen, Oct 09 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..124340

Crossrefs

Cf. A155043, A261089, A262503, A263078, A263079, A263080, A263082.

Programs

Mathematica

a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; Table[k = 3 n;
While[a@ k >= a@ n, k--]; k, {n, 96}] (* Michael De Vlieger, Oct 13 2015 *)

PARI

allocatemem((2^31)+(2^30));
uplim1 = 36756720 + 640; \\ = A002182(53) + A002183(53).
uplim2 = 36756720; \\ = A002182(53).
uplim3 = 32432400; \\ = A002182(52). Really just some Ad Hoc value smaller than above.
v155043 = vector(uplim1);
vother = vector(uplim3); \\ Contains A262503 and A263082 in succession.
v155043[1] = 1; v155043[2] = 1;
for(i=3, uplim1, v155043[i] = 1 + v155043[i-numdiv(i)]; if(!(i%1048576),print1(i,", ")));
A155043 = n -> if(!n,n,v155043[n]);
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.
print("uplim2=", uplim2, " uplim3=", uplim3, " maxlen=", maxlen);
\\ Then we convert it to A263082:
m = 0; for(i=1, maxlen, m = max(m, vother[i]); vother[i] = m; if(!(i%1048576),print1(i,", ")));
A263082 = n -> if(!n,n,vother[n]);
A263077 = n -> A263082(A155043(n)-1);
\\ Finally we can compute A263077:
for(i=1, uplim3, write("b263077.txt", i, " ", A263077(i)); );

Formula

a(n) = A263082(A155043(n)-1).