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 1-3 of 3 results.

A346242 Dirichlet inverse of A324198, where A324198(n) = gcd(n, A276086(n)).

Original entry on oeis.org

1, -1, -3, 0, -1, 5, -1, 0, 6, -3, -1, -2, -1, 1, -9, 0, -1, -16, -1, 4, 3, 1, -1, 0, -24, 1, -12, 0, -1, 43, -1, 0, 3, 1, -5, 14, -1, 1, 3, 0, -1, -11, -1, 0, 54, 1, -1, 0, -6, 32, 3, 0, -1, 44, -3, -6, 3, 1, -1, -50, -1, 1, -24, 0, 1, -5, -1, 0, 3, -15, -1, -4, -1, 1, 96, 0, -5, -5, -1, 0, 24, 1, -1, 8, -3, 1, 3, 0, -1
Offset: 1

Views

Author

Antti Karttunen, Jul 13 2021

Keywords

Links

Crossrefs

Cf. A276086, A324198, A346243.
Cf. A008966 (parity of terms), A005117 (positions of odd terms), A013929 (of even terms), A045344 (of -1's, at least a subset of them), A354810 (of 0's), A354811 (of 1's), A354812 (of 2's), A354813 (of 3's), A354814 (of 4's), A354822 (of -2's).
Cf. also A354347, A354348, A354823, A354824.

Programs

  • PARI
    up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
v346242 = DirInverseCorrect(vector(up_to,n,A324198(n)));
A346242(n) = v346242[n];

Formula

a(n) = A346243(n) - A324198(n).
From Antti Karttunen, Jun 09 2022: (Start)
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA324198(n/d) * a(d).
For all n >= 1, A000035(a(n)) = A008966(n).
For all n >= 1, a(A045344(n)) = -1.
(End)

A354810 Positions of zeros in A346242.

Original entry on oeis.org

4, 8, 16, 24, 28, 32, 40, 44, 48, 52, 64, 68, 76, 80, 88, 92, 96, 104, 116, 121, 124, 128, 136, 144, 148, 152, 160, 164, 169, 172, 176, 184, 188, 192, 208, 212, 232, 236, 240, 244, 248, 256, 268, 272, 284, 288, 289, 292, 296, 304, 312, 316, 320, 328, 332, 338, 344, 356, 361, 364, 368, 376, 384, 388, 404, 408, 412, 416
Offset: 1

Views

Author

Antti Karttunen, Jun 07 2022

Keywords

Links

Crossrefs

Cf. A346242, A354820 (characteristic function).
Cf. also A354811, A354812, A354813, A354814, A354822.

Programs

A354812 Positions of +2's in A346242.

Original entry on oeis.org

132, 156, 204, 228, 276, 348, 372, 444, 492, 516, 564, 636, 708, 732, 804, 852, 876, 948, 996, 1068, 1164, 1212, 1236, 1284, 1308, 1356, 1524, 1572, 1644, 1668, 1788, 1812, 1884, 1956, 2004, 2076, 2148, 2172, 2292, 2316, 2364, 2388, 2532, 2676, 2724, 2748, 2796, 2868, 2892, 3012, 3084, 3156, 3228, 3252, 3324, 3372
Offset: 1

Views

Author

Antti Karttunen, Jun 07 2022

Keywords

Comments

Question: Are all terms even?

Crossrefs

Cf. A346242.
Cf. also A354814, A354822.

Programs

Showing 1-3 of 3 results.

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