A349632 Dirichlet convolution of A250469 with A346234, which is Dirichlet inverse of A003961.

1, 0, 0, 0, 0, 0, 0, -6, 0, 6, 0, -12, 0, 6, 0, -18, 0, -24, 0, -24, 0, 24, 0, 0, 0, 24, -60, -36, 0, -48, 0, -42, 20, 42, 0, 12, 0, 42, 10, -12, 0, -72, 0, -60, -60, 48, 0, 24, 0, -42, 30, -72, 0, 84, 0, -12, 30, 78, 0, 120, 0, 72, -120, -90, 0, -180, 0, -96, 30, -132, 0, 48, 0, 96, -60, -108, 0, -174, 0, 12, -120

Offset

1,8

Comments

Note that for n = 2..36, a(n) = -A349631(n).

Dirichlet convolution of this sequence with A003972 is A347376.

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences generated by sieves

Formula

a(n) = Sum_{d|n} A250469(d) * A346234(n/d).

Prog

(PARI)
up_to = 20000;
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
v078898 = ordinal_transform(vector(up_to, n, A020639(n)));
A078898(n) = v078898[n];
A250469(n) = if(1==n, n, my(spn = nextprime(1+A020639(n)), c = A078898(n), k = 0); while(c, k++; if((1==k)||(A020639(k)>=spn), c -= 1)); (k*spn));
A346234(n) = (moebius(n)*A003961(n));
A349632(n) = sumdiv(n, d, A250469(n/d)*A346234(d));

Crossrefs

Cf. A003961, A250469, A346234, A349631 (Dirichlet inverse).

Cf. also A003972, A347376, A349382.

Cf. also arrays A083221, A246278, A249821, A249822 and permutations A250245, A250246.

Sequence in context: A198368 A064373 A195290 * A349631 A347377 A280692

Adjacent sequences: A349629 A349630 A349631 * A349633 A349634 A349635

Keyword

sign

Author

Antti Karttunen, Nov 27 2021

Status

approved