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A069929 Number of k, 1 <= k <= n, such that k^3+1 divides n^3+1. 2
1, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2, 1, 3, 1, 2, 3, 3, 1, 3, 1, 3, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 5, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 3, 2, 2, 2, 3, 1, 2, 3, 4, 1, 3, 1, 2, 2, 4, 1, 3, 1, 2, 2, 2, 1, 5, 1, 2, 2, 3, 1, 4, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 4, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
Conjecture: (1/n)*Sum_{k=1..n} a(k) = C*log(log(n)) + o(log(log(n)) with 1 < C < 3/2.
EXAMPLE
a(5) = 3 because among the numbers 1^3+1 = 2, 2^3+1 = 9, 3^3+1 = 28, 4^3+1 = 65, and 5^3 + 1 = 126, only 3 of them (2, 9, 126) divide 5^3+1 = 126. - Petros Hadjicostas, Sep 18 2019
MAPLE
a:= n-> add(`if`(irem(n^3+1, k^3+1)=0, 1, 0), k=1..n):
seq(a(n), n=1..120); # Alois P. Heinz, Sep 18 2019
PROG
(PARI) for(n=1, 150, print1(sum(i=1, n, if((n^3+1)%(i^3+1), 0, 1)), ", "))
CROSSREFS
Cf. A066743.
Sequence in context: A319136 A320777 A350380 * A304081 A101312 A241273
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 05 2002
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)