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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 (list; graph; refs; listen; history; text; internal format)
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[n-1]%2, v[n]=v[n-1] + factor(v[n-1])[1, 1], v[n]=v[n-1] - 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

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Last modified April 14 07:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)