|
|
A343511
|
|
a(n) = 1 + Sum_{d|n, d < n} a(d)^2.
|
|
2
|
|
|
1, 2, 2, 6, 2, 10, 2, 42, 6, 10, 2, 146, 2, 10, 10, 1806, 2, 146, 2, 146, 10, 10, 2, 23226, 6, 10, 42, 146, 2, 314, 2, 3263442, 10, 10, 10, 42814, 2, 10, 10, 23226, 2, 314, 2, 146, 146, 10, 2, 542731938, 6, 146, 10, 146, 2, 23226, 10, 23226, 10, 10, 2, 141578, 2, 10, 146, 10650056950806, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) depends only on the prime signature of n (see formulas). - Bernard Schott, Apr 24 2021
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x / (1 - x) + Sum_{n>=1} a(n)^2 * x^(2*n) / (1 - x^n).
a(A006881(n)) = 10 for signature [1, 1].
a(A054753(n)) = 146 for signature [2, 1].
a(A007304(n)) = 314 for signature [1, 1, 1].
a(A065036(n)) = 23226 for signature [3, 1].
a(A085986(n)) = 42814 for signature [2, 2].
a(A085987(n)) = 141578 for signature [2, 1, 1]. (End)
|
|
MAPLE
|
a:= proc(n) option remember;
1+add(a(d)^2, d=numtheory[divisors](n) minus {n})
end:
|
|
MATHEMATICA
|
a[n_] := a[n] = 1 + Sum[If[d < n, a[d]^2, 0], {d, Divisors[n]}]; Table[a[n], {n, 65}]
|
|
PROG
|
(Python)
from functools import lru_cache
from sympy import divisors
@lru_cache(maxsize=None)
(PARI) lista(nn) = {my(va = vector(nn)); for (n=1, nn, va[n] = 1 + sumdiv(n, d, if (d<n, va[d]^2)); ); va; } \\ Michel Marcus, Apr 18 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|