A347376 Möbius transform of A250469.

1, 2, 4, 6, 6, 8, 10, 12, 20, 18, 12, 12, 16, 26, 24, 24, 18, 16, 22, 24, 40, 48, 28, 24, 42, 56, 40, 36, 30, 24, 36, 48, 68, 78, 60, 36, 40, 86, 74, 48, 42, 32, 46, 60, 60, 104, 52, 48, 110, 78, 102, 72, 58, 68, 72, 72, 118, 138, 60, 48, 66, 144, 80, 96, 96, 52, 70, 96, 142, 84, 72, 72, 78, 176, 108, 108, 120, 70

Offset: 1

Author

Antti Karttunen, Sep 01 2021

Keywords

• nonn

Comments

Question: Are all terms positive?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves

Crossrefs

Cf. A003972, A008683, A020639, A078898, A250469, A347377.

Cf. also A346479.

Programs

PARI

up_to = 10000;
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; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
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));
A347376(n) = sumdiv(n,d,moebius(n/d)*A250469(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A250469(d).

a(n) = A003972(n) - A347377(n).