

A281488


a(n) = Sum_{d divides (n2), 1 <= d < n} a(d).


3



1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 3, 0, 2, 1, 2, 2, 3, 1, 4, 1, 3, 0, 5, 1, 7, 1, 7, 1, 5, 0, 6, 1, 9, 2, 11, 1, 9, 1, 8, 0, 12, 0, 15, 0, 11, 1, 13, 0, 17, 1, 18, 2, 17, 1, 17, 0, 24, 0, 28, 1, 21, 0, 22
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OFFSET

1,18


COMMENTS

a(1) = 1, any other choice simply adds a factor to all terms.
The even bisection of the sequence seems to behave similarly to A281487 with similar asymptotics for a(n). However, the odd bisection shows oscillations with increasing intervals between crossing the zero and increasing amplitude.


LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 1..20000
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625, Dec 08, 2020


FORMULA

a(1) = 1,
a(n) = Sum_{d(n2), 1 <= d < n} a(d) for n>1.


PROG

a = [1]
for n in range(2, 100):
a.append(sum(a[d1] for d in range(1, n) if (n2)%d == 0))
print(a)


CROSSREFS

Cf. A007439 (same formula with overall + instead of ), A281487 (same formula with (n1) instead of (n2)), A000123.
Sequence in context: A125073 A325310 A308881 * A071461 A091829 A194188
Adjacent sequences: A281485 A281486 A281487 * A281489 A281490 A281491


KEYWORD

sign,easy,look,hear


AUTHOR

Andrey Zabolotskiy, Jan 22 2017


STATUS

approved



