OFFSET
1,3
COMMENTS
For terms m of A007369, numbers m such that sigma(x) = m has no solution, as well as for m = 1, a(m) = 1.
See A257670 for more information, examples, etc. - M. F. Hasler, Nov 19 2019
Records are: a(1) = 1 = a(2), a(3) = 2, a(4) = 3, a(7) = 4, a(8) = 5, a(15) = 6, a(24) = 11, a(60) = 15, a(120) = 16, a(168) = 22 = a(336), a(360) = 26, a(480) = 39, a(1344) = 43, a(1512) = 54, a(1920) = 57, a(2016) = 65, a(2880) = 70, a(4800) = 80, a(5040) = 88, a(6552) = 93, a(8064) = 125, ... - M. F. Hasler, Nov 20 2019
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..10000, Nov 20 2019
M. Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invsigma.gp, Oct. 2005
G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 91-100.
FORMULA
a(A007369(n)) = 1.
EXAMPLE
For n = 2, a(2) = 1, since there is no x such that sigma(x) = 2, so the subtree with root 2 is reduced to a single node: 2.
For n = 3, since sigma(2) = 3, the tree with root 3 has 2 nodes: 2 and 3, hence a(3) = 2.
PROG
(PARI) A257669_vec(N)={my(C=Map(), s, c); vector(N, n, mapput(C, s=sigma(n), if(mapisdefined(C, s), mapget(C, s))+ c=if(mapisdefined(C, n), mapget(C, n) + mapdelete(C, n))+1); c)} \\ M. F. Hasler, Nov 20 2019
(PARI) apply( A257669(n)=if(n>1, vecsum(apply(self, invsigma(n))))+1, [1..99]) \\ See Alekseyev-link for invsigma(). - M. F. Hasler, Nov 20 2019, replacing earlier code from Michel Marcus
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, May 03 2015
STATUS
approved