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

Author

Antti Karttunen, Nov 25 2024

Keywords

• nonn

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

Crossrefs

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

Cf. also A067824.

Odd bisection is not equal to A278223.

Programs

PARI

memoA345182 = Map();
A345182(n) = if(n<=2, n%2, my(v); if(mapisdefined(memoA345182,n,&v), v, v = sumdiv(n,d,if(dA345182(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,(dA378223list(up_to);
A378223(n) = v378223[n];

Formula

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

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