A354352 -id:A354352 - cp's OEIS frontend

A354351 Dirichlet inverse of A108951, primorial inflation of n.

1, -2, -6, 0, -30, 12, -210, 0, 0, 60, -2310, 0, -30030, 420, 180, 0, -510510, 0, -9699690, 0, 1260, 4620, -223092870, 0, 0, 60060, 0, 0, -6469693230, -360, -200560490130, 0, 13860, 1021020, 6300, 0, -7420738134810, 19399380, 180180, 0, -304250263527210, -2520, -13082761331670030, 0, 0, 446185740, -614889782588491410

Offset: 1

Antti Karttunen, Jun 05 2022

Multiplicative with a(p^e) = 0 if e > 1, and -A034386(p) otherwise.

Cf. A002110, A008683, A013929 (positions of 0's), A034386, A108951, A354352.

Cf. also A347379, A354186, A354349, A354359, A354365, A354366.

A002110(n) = prod(i=1,n,prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951
A354351(n) = (moebius(n)*A108951(n));

a(n) = A008683(n) * A108951(n).
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A108951(n/d) * a(d).
a(n) = A354352(n) - A108951(n).

A354867 Sum of A122111 and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 4, 0, 16, 0, 4, 16, 32, 0, 0, 0, 64, 64, 9, 0, -12, 0, 0, 128, 128, 0, 28, 64, 256, 8, 0, 0, -120, 0, 8, 256, 512, 256, 74, 0, 1024, 512, 56, 0, -240, 0, 0, -96, 2048, 0, -4, 256, -84, 1024, 0, 0, 120, 512, 112, 2048, 4096, 0, 284, 0, 8192, -192, 20, 1024, -480, 0, 0, 4096, -552, 0, -64, 0, 16384, -264, 0, 1024

Offset: 1

Antti Karttunen, Jun 09 2022

sign

Antti Karttunen, Table of n, a(n) for n = 1..12000
Index entries for sequences computed from indices in prime factorization

Cf. A122111, A354866.

Cf. also A354352.

A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
memoA354866 = Map();
A354866(n) = if(1==n,1,my(v); if(mapisdefined(memoA354866,n,&v), v, v = -sumdiv(n,d,if(dA122111(n/d)*A354866(d),0)); mapput(memoA354866,n,v); (v)));
A354867(n) = (A122111(n)+A354866(n));

a(n) = A122111(n) + A354866(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A122111(d) * A354866(n/d).

cp's OEIS Frontend

A354351 Dirichlet inverse of A108951, primorial inflation of n.

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