cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A354351 Dirichlet inverse of A108951, primorial inflation of n.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 05 2022

Keywords

Comments

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

Links

Crossrefs

Cf. A002110, A008683, A013929 (positions of 0's), A034386, A108951, A354352.
Cf. also A347379, A354186, A354349, A354359, A354365, A354366.

Programs

Formula

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).

A354359 Dirichlet inverse of A124859.

Original entry on oeis.org

1, -2, -2, -2, -2, 4, -2, -14, -2, 4, -2, 4, -2, 4, 4, -110, -2, 4, -2, 4, 4, 4, -2, 28, -2, 4, -14, 4, -2, -8, -2, -1526, 4, 4, 4, 4, -2, 4, 4, 28, -2, -8, -2, 4, 4, 4, -2, 220, -2, 4, 4, 4, -2, 28, 4, 28, 4, 4, -2, -8, -2, 4, 4, -20858, 4, -8, -2, 4, 4, -8, -2, 28, -2, 4, 4, 4, 4, -8, -2, 220, -110, 4, -2, -8
Offset: 1

Views

Author

Antti Karttunen, Jun 05 2022

Keywords

Comments

Multiplicative because A124859 is.

Links

Crossrefs

Cf. A002110, A124859.
Cf. also A354186, A354349, A354351, A354358.

Programs

  • PARI
    A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859
memoA354359 = Map();
A354359(n) = if(1==n,1,my(v); if(mapisdefined(memoA354359,n,&v), v, v = -sumdiv(n,d,if(dA124859(n/d)*A354359(d),0)); mapput(memoA354359,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A124859(n/d) * a(d).

A354866 Dirichlet inverse of A122111.

Original entry on oeis.org

1, -2, -4, 1, -8, 10, -16, -1, 7, 20, -32, -10, -64, 40, 46, 2, -128, -27, -256, -20, 92, 80, -512, 14, 37, 160, -17, -40, -1024, -150, -2048, -3, 184, 320, 202, 53, -4096, 640, 368, 28, -8192, -300, -16384, -80, -146, 1280, -32768, -26, 175, -129, 736, -160, -65536, 85, 404, 56, 1472, 2560, -131072, 242, -262144
Offset: 1

Views

Author

Antti Karttunen, Jun 09 2022

Keywords

Links

Crossrefs

Cf. A122111, A354867, A354868 (parity), A354869 (positions of odd terms).
Cf. also A354186, A354349, A354351, A354359, A354826.

Programs

  • PARI
    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)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA122111(n/d) * a(d).
a(n) = A354867(n) - A122111(n).

A354826 Dirichlet inverse of A238745.

Original entry on oeis.org

1, -2, -2, 0, -2, 5, -2, 0, 0, 5, -2, -2, -2, 5, 5, 0, -2, -2, -2, -2, 5, 5, -2, 0, 0, 5, 0, -2, -2, -17, -2, 0, 5, 5, 5, 8, -2, 5, 5, 0, -2, -17, -2, -2, -2, 5, -2, 0, 0, -2, 5, -2, -2, 0, 5, 0, 5, 5, -2, 16, -2, 5, -2, 0, 5, -17, -2, -2, 5, -17, -2, -8, -2, 5, -2, -2, 5, -17, -2, 0, 0, 5, -2, 16, 5, 5, 5, 0, -2, 16
Offset: 1

Views

Author

Antti Karttunen, Jun 09 2022

Keywords

Links

Crossrefs

Cf. A238745.
Cf. also A354349, A354359.

Programs

  • PARI
    A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A238745(n) = A181819(A124859(n));
memoA354826 = Map();
A354826(n) = if(1==n,1,my(v); if(mapisdefined(memoA354826,n,&v), v, v = -sumdiv(n,d,if(dA238745(n/d)*A354826(d),0)); mapput(memoA354826,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA238745(n/d) * a(d).
Showing 1-4 of 4 results.

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