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A185615 Numbers k that divide A000201(k)^m for some integer m > 0, where A000201 is the lower Wythoff sequence. 3
1, 4, 8, 25, 50, 108, 169, 243, 256, 338, 486, 512, 729, 768, 972, 1024, 1156, 1215, 2312, 3375, 5000, 7921, 8192, 8748, 10000, 12800, 15000, 15842, 20000, 25000, 50176, 54289, 85184, 88209, 100352, 104976, 108578, 131072, 176418, 177147 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let k = p_1^{e_1} * p_2^{e_2} * ... * p_r^{e_r}. Then k is in this sequence iff p_1*p_2*...*p_r divides A000201(k).

Many of these terms are powers of Fibonacci numbers.

Perhaps this is expected, since A000201(k) involves floor(k*phi).

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

For n=8, A000201(8)=12. Since 8 divides 12^2, 8 is in this sequence.

For n=9, A000201(9)=14. Since 9 cannot divide 14^m for any m, 9 is not in this sequence.

PROG

(Python)

from math import isqrt, prod

from itertools import count, islice

from sympy import primefactors

def A185615_gen(startvalue=1): # generator of terms >= startvalue

    return filter(lambda n: not (n+isqrt(5*n**2)>>1)%prod(primefactors(n)), count(max(startvalue, 1)))

A185615_list = list(islice(A185615_gen(), 30)) # Chai Wah Wu, Aug 10 2022

CROSSREFS

Cf. A000201, A185616, A185617.

Sequence in context: A131637 A163143 A154586 * A068367 A292548 A000964

Adjacent sequences:  A185612 A185613 A185614 * A185616 A185617 A185618

KEYWORD

nonn

AUTHOR

Paul D. Hanna and Sean A. Irvine, Jan 31 2011

STATUS

approved

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Last modified September 30 06:13 EDT 2022. Contains 357099 sequences. (Running on oeis4.)