

A286011


a(1)=1, and for n>1, a(n) is the maximum number of iterations of sigma resulting in n, starting at some integer k; or 0 if n cannot be reached from any k.


1



1, 0, 1, 2, 0, 1, 3, 4, 0, 0, 0, 2, 1, 2, 5, 0, 0, 1, 0, 1, 0, 0, 0, 6, 0, 0, 0, 3, 0, 1, 1, 2, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 1, 0, 0, 7, 0, 1, 3, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2
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OFFSET

1,4


COMMENTS

a(n)=0 for n in A007369 and a(n)>0 for n in A002191.
Records are found at indices given by A007497.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

a(4)=2 because 4=sigma(3), but also sigma(sigma(2)) with 2 iterations.
a(7)=3 because 7=sigma(4), but also sigma(sigma(3)), and sigma(sigma(sigma(2))), with 3 iterations.


MAPLE

N:= 100: # to get a(1)..a(N)
V:= Vector(N):
for n from 1 to N do
s:= numtheory:sigma(n);
if s <= N then V[s]:= max(V[s], V[n]+1) fi
od:
convert(V, list); # Robert Israel, May 01 2017


PROG

(PARI) a(n) = {if (n==1, return(1)); vn = vector(n1, k, k+1); nb = 0; knb = 0; ok = 1; while(ok, nb++; vn = vector(#vn, k, sigma(vn[k])); svn = Set(vn); if (#select(x>x==n, svn), knb = nb); if (!#select(x>x<=n, svn), ok = 0); ); knb; }


CROSSREFS

Cf. A000203, A002191, A007369, A007497, A257670.
Sequence in context: A124031 A289229 A263097 * A241954 A049600 A318602
Adjacent sequences: A286008 A286009 A286010 * A286012 A286013 A286014


KEYWORD

nonn


AUTHOR

Michel Marcus, Apr 30 2017


STATUS

approved



