A378223 Inverse Möbius transform of A345182.

1, 1, 2, 2, 2, 4, 2, 4, 4, 4, 2, 10, 2, 4, 6, 8, 2, 12, 2, 10, 6, 4, 2, 24, 4, 4, 8, 10, 2, 20, 2, 16, 6, 4, 6, 36, 2, 4, 6, 24, 2, 20, 2, 10, 16, 4, 2, 56, 4, 12, 6, 10, 2, 32, 6, 24, 6, 4, 2, 62, 2, 4, 16, 32, 6, 20, 2, 10, 6, 20, 2, 100, 2, 4, 16, 10, 6, 20, 2, 56, 16, 4, 2, 62, 6, 4, 6, 24, 2, 72, 6, 10, 6, 4, 6

Offset

1,3

Comments

Apparently the Dirichlet convolution of A002131 and A323910. - Antti Karttunen, Nov 30 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} A345182(d).

For n > 2, a(n) = 2*A345182(n).

Prog

(PARI)
memoA345182 = Map();
A345182(n) = if(n<=2, n%2, my(v); if(mapisdefined(memoA345182, n, &v), v, v = sumdiv(n, d, if(d<n, A345182(d), 0)); mapput(memoA345182, n, v); (v)));
A378223(n) = sumdiv(n, d, A345182(d));
(PARI)
up_to = 20000;
A378223list(up_to_n) = { my(v=vector(up_to_n)); v[1] = 1; v[2] = 0; for(n=3, up_to_n, v[n] = 1+sumdiv(n, d, (d<n)*v[d])); v[2]++; (v); };
v378223 = A378223list(up_to);
A378223(n) = v378223[n];

Crossrefs

Cf. A002131, A323910, A345182, A378224 (Dirichlet inverse).

Cf. also A067824.

Odd bisection is not equal to A278223.

Sequence in context: A072056 A356831 A066012 * A063375 A064129 A005137

Adjacent sequences: A378220 A378221 A378222 * A378224 A378225 A378226

Keyword

nonn

Author

Antti Karttunen, Nov 25 2024

Status

approved