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A133565 a(1)=1. a(n+1) = sum{k=non-isolated divisors of n} a(k). A non-isolated divisor, k, of n is a positive divisor of n where (k-1) or (k+1) divides n. 3
1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

a(2n) = 0 since 2n-1 has no non-isolated divisors. - Ray Chandler

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

EXAMPLE

The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are adjacent and 4 and 5 are adjacent. So the non-isolated divisors of 20 are 1,2, 4,5. Therefore a(21) = a(1) + a(2) + a(4) + a(5) = 1 + 0 + 0 + 1 = 2.

PROG

(PARI) A133565(n) = if(1==n, n, sumdiv(n-1, d, if((!((n-1)%(1+d))) || ((d>1)&&(!((n-1)%(d-1)))), A133565(d), 0))); \\ Antti Karttunen, Dec 19 2018

CROSSREFS

Cf. A132748, A133564.

Sequence in context: A276084 A230403 A248908 * A239704 A168570 A267860

Adjacent sequences:  A133562 A133563 A133564 * A133566 A133567 A133568

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 16 2007

EXTENSIONS

Extended by Ray Chandler, Jun 25 2008

STATUS

approved

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Last modified May 27 02:54 EDT 2019. Contains 323597 sequences. (Running on oeis4.)