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A378646
Dirichlet convolution of A000027 and A378643.
4
1, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 4, 1, 3, 3, 8, 1, 4, 1, 6, 3, 3, 1, 8, 2, 3, 4, 8, 1, 1, 1, 16, 3, 3, 3, 10, 1, 3, 3, 10, 1, 1, 1, 8, 8, 3, 1, 16, 2, 8, 3, 8, 1, 12, 3, 12, 3, 3, 1, 10, 1, 3, 8, 32, 3, 1, 1, 8, 3, 9, 1, 16, 1, 3, 8, 8, 3, 1, 1, 20, 8, 3, 1, 8, 3, 3, 3, 16, 1, 14, 3, 8, 3, 3, 3, 32, 1, 8, 8, 14, 1, 1, 1, 18, 13
OFFSET
1,4
COMMENTS
First negative value is a(140) = -2.
Odd bisection is not A352063: a(472*2 + 1) = 102 != A352063(472) = A074206(945) = 132. Note that 945 is the first odd abundant number, A005231.
LINKS
FORMULA
a(n) = Sum_{d|n} d*A378643(n/d).
a(n) = A074206(n) if n is a non-abundant number (A263837), and apparently never when n is abundant, A005101.
PROG
(PARI) A378646(n) = sumdiv(n, d, d*A378643(n/d));
CROSSREFS
Cf. A000027, A005101, A005231, A074206, A103977, A378643, A378645 (Dirichlet inverse).
Sequence in context: A249336 A067004 A117920 * A079617 A079616 A292587
KEYWORD
sign
AUTHOR
Antti Karttunen, Dec 03 2024
STATUS
approved