

A281487


a(n+1) = Sum_{dn} a(d).


4



1, 1, 0, 1, 1, 2, 2, 3, 4, 5, 4, 5, 8, 9, 7, 9, 13, 14, 12, 13, 18, 21, 17, 18, 29, 31, 23, 28, 36, 37, 36, 37, 50, 55, 42, 46, 64, 65, 53, 62, 83, 84, 75, 76, 94, 107, 90, 91, 129, 132, 107, 121, 145, 146, 135, 141, 180, 193, 157
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OFFSET

1,6


COMMENTS

a(1) = 1, any other choice simply adds a factor to all terms.
Observations: sign of a(n) is (1)^n, the subsequences a(n) with n = 1, 2 mod 4 and a(n) with n = 3, 0 mod 4 both grow at n>5. Both these subsequences seem to share the asymtotics with A003238 (and hence A000123): log(a(n)) is approximately proportional to (log(n/log(n)))^2; however, the factor is much less than log(4).
There is a family of sequences with the formula a(n) = s*Sum_{d(nk), 1<=d<n} a(d). For s=+1 and k = 0,1,2, these are A002033, A003238, A007439. For s=1 and k = 0,1,2, these are the Möbius function A008683, this sequence, and A281488.


LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 1..20000


FORMULA

a(1) = 1.
a(n+1) = Sum_{dn} a(d) for n>=1.
a(n+1) = Sum_{dn} a(d)*(1)^(d+n) for n>=1.


EXAMPLE

a(9) = (a(1)+a(2)+a(4)+a(8)) = (1113) = 4.


PROG

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


CROSSREFS

Cf. A003238, A281488, A000123.
Sequence in context: A030564 A205114 A293428 * A224401 A252462 A094457
Adjacent sequences: A281484 A281485 A281486 * A281488 A281489 A281490


KEYWORD

sign,easy


AUTHOR

Andrey Zabolotskiy, Jan 22 2017


STATUS

approved



