

A168007


Jumping divisor sequence (see Comments lines for definition).


3



1, 2, 4, 3, 6, 5, 10, 9, 12, 11, 22, 21, 24, 23, 46, 45, 48, 47, 94, 93, 96, 95, 100, 99, 102, 101, 202, 201, 204, 203, 210, 209, 220, 219, 222, 221, 234, 233, 466, 465, 468, 467, 934, 933, 936, 935, 940, 939, 942, 941, 1882, 1881, 1884, 1883, 1890, 1889, 3778, 3777, 3780, 3779, 7558, 7557, 7560, 7559
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OFFSET

1,2


COMMENTS

Consider the diagram with overlapping periodic curves that appears in the Links section (figure 2). The number of curves that contain the point [n,0] equals the number of divisors of n. The curve of diameter d represents the divisor d of n. Now consider only the lower part of the diagram (figure 3). Starting from point [1,0] we continue our journey walking along the semicircumference with smallest diameter not used previously (see the illustration of initial terms, figure 1). The sequence is formed by the values of n where the trajectory intercepts the x axis.  Omar E. Pol, Jan 14 2019


LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..1000
Omar E. Pol, Illustration of initial terms (Fig. 1)
Omar E. Pol, Periodic curves and tau(n) (Fig. 2)
Omar E. Pol, Periodic curves and tau(n), lower part upside down (Fig. 3)


FORMULA

a(1) = 1; if a(n) is an even composite number then a(n+1) = a(n)  1; otherwise a(n+1) = a(n) + A020639(a(n)).  Omar E. Pol, Jan 13 2019


PROG

(PARI) lista(nn) = {my(v=vector(nn, i, if(i<4, 2^i/2))); for(n=4, nn, if(v[n1]%2, v[n]=v[n1] + factor(v[n1])[1, 1], v[n]=v[n1]  1)); v; } \\ Jinyuan Wang, Mar 14 2020


CROSSREFS

Cf. A000005, A002808, A020639, A004280, A168008, A168009.
Sequence in context: A116533 A087559 A193298 * A328108 A091850 A332450
Adjacent sequences: A168004 A168005 A168006 * A168008 A168009 A168010


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Nov 19 2009


EXTENSIONS

More terms from Omar E. Pol, Jan 12 2019


STATUS

approved



