|
| |
|
|
A284900
|
|
a(n) = Sum_{d|n} (-1)^(n/d+1)*d^4.
|
|
10
|
|
|
|
1, 15, 82, 239, 626, 1230, 2402, 3823, 6643, 9390, 14642, 19598, 28562, 36030, 51332, 61167, 83522, 99645, 130322, 149614, 196964, 219630, 279842, 313486, 391251, 428430, 538084, 574078, 707282, 769980, 923522, 978671, 1200644, 1252830, 1503652, 1587677
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Multiplicative because this sequence is the Dirichlet convolution of A000583 and A062157 which are both multiplicative. - Andrew Howroyd, Jul 20 2018
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 1..10000
J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).
Index entries for sequences mentioned by Glaisher
|
|
|
FORMULA
|
G.f.: Sum_{k>=1} k^4*x^k/(1 + x^k). - Ilya Gutkovskiy, Apr 07 2017
|
|
|
MATHEMATICA
|
Table[Sum[(-1)^(n/d + 1)*d^4, {d, Divisors[n]}], {n, 50}] (* Indranil Ghosh, Apr 05 2017 *)
|
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, (-1)^(n/d + 1)*d^4); \\ Indranil Ghosh, Apr 05 2017
(Python)
from sympy import divisors
print [sum([(-1)**(n/d + 1)*d**4 for d in divisors(n)]) for n in range(1, 51)] # Indranil Ghosh, Apr 05 2017
|
|
|
CROSSREFS
|
Sum_{d|n} (-1)^(n/d+1)*d^k: A000593 (k=1), A078306 (k=2), A078307 (k=3), this sequence (k=4), A284926 (k=5), A284927 (k=6).
Cf. A000583, A062157.
Sequence in context: A213552 A060581 A253222 * A065103 A279395 A270768
Adjacent sequences: A284897 A284898 A284899 * A284901 A284902 A284903
|
|
|
KEYWORD
|
nonn,mult,changed
|
|
|
AUTHOR
|
Seiichi Manyama, Apr 05 2017
|
|
|
STATUS
|
approved
|
| |
|
|
