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.

A346250 Sum of -A252748 and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 1, 0, 2, 0, -3, 1, 6, 0, -11, 0, 6, 6, -17, 0, -23, 0, -17, 6, 18, 0, -39, 9, 18, -15, -25, 0, -48, 0, -51, 18, 30, 18, -49, 0, 30, 18, -77, 0, -72, 0, -35, -61, 34, 0, -85, 9, -31, 30, -43, 0, -123, 54, -97, 30, 54, 0, -117, 0, 50, -77, -89, 54, -96, 0, -53, 34, -104, 0, -19, 0, 66, -55, -61, 54, -120, 0
Offset: 1

Views

Author

Antti Karttunen, Jul 19 2021

Keywords

Links

Crossrefs

Cf. A003961, A252748, A346248.
Cf. also A323911, A346236, A346247, A346255.

Programs

  • PARI
    up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A252748(n) = (A003961(n) - (2*n));
v346248 = DirInverseCorrect(vector(up_to,n,-A252748(n)));
A346248(n) = v346248[n];
A346250(n) = (A346248(n)-A252748(n));

Formula

a(n) = A346248(n) - A252748(n).

A346235 Dirichlet inverse of A341530, gcd(n*sigma(A003961(n)), sigma(n)*A003961(n)).

Original entry on oeis.org

1, -1, -2, 0, -2, -32, -4, -4, 3, 2, -2, 34, -2, -16, -112, 8, -2, 125, -4, 0, 8, 0, -6, -128, 3, -14, -8, -124, -2, 8, -2, -10, -4, 2, -320, 920, -2, -4, 4, 8, -2, 64, -4, -358, 430, -12, -6, 528, -3, -5, -352, 16, -6, -368, -48, 224, 0, 2, -2, 104, -2, -12, -12, 28, -4, 16, -4, 0, -36, 400, -2, -440, -2, -2, 450, 8, -248, 128
Offset: 1

Views

Author

Antti Karttunen, Jul 11 2021

Keywords

Links

Crossrefs

Cf. A000203, A003961, A341530, A346236.
Cf. also A346246, A346248, A346254.

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(dA003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
v346235 = DirInverseCorrect(vector(up_to,n,A341530(n)));
A346235(n) = v346235[n];

A346255 Sum of A336849 and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 9, 0, 30, 0, 27, 25, 42, 0, -15, 0, 66, 70, 81, 0, -25, 0, 63, 110, 78, 0, 45, 49, 102, 125, -33, 0, -140, 0, 243, 130, 114, 154, 625, 0, 138, 170, 189, 0, -440, 0, 117, 175, 174, 0, -81, 121, 147, 190, -51, 0, 625, 182, 99, 230, 186, 0, 315, 0, 222, 275, 729, 238, -260, 0, 171, 290, -308, 0, 15, 0, 246, 245, -69, 286
Offset: 1

Views

Author

Antti Karttunen, Jul 19 2021

Keywords

Links

Crossrefs

Cf. A000203, A003961, A003973, A336849, A346254.
Cf. also A346236, A346247, A346250.

Programs

  • PARI
    up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A336849(n) = { my(u=A003961(n)); (u/gcd(u, sigma(u))); };
v346254 = DirInverseCorrect(vector(up_to,n,A336849(n)));
A346254(n) = v346254[n];
A346255(n) = (A336849(n)+A346254(n));

Formula

a(n) = A336849(n) + A346254(n).

A347097 a(1) = 2; and for n > 1, a(n) = A341512(n) + A347096(n).

Original entry on oeis.org

2, 0, 0, 1, 0, 4, 0, 21, 4, 4, 0, 110, 0, 8, 8, 259, 0, 224, 0, 154, 16, 4, 0, 1548, 4, 8, 176, 316, 0, 592, 0, 2445, 8, 4, 16, 4312, 0, 8, 16, 2450, 0, 1216, 0, 382, 640, 12, 0, 15532, 16, 408, 8, 616, 0, 6708, 8, 5064, 16, 4, 0, 12272, 0, 12, 1312, 19543, 16, 1504, 0, 754, 24, 1568, 0, 50561, 0, 8, 832, 1060, 16
Offset: 1

Views

Author

Antti Karttunen, Aug 19 2021

Keywords

Comments

Sum of {the pointwise sum of A341512 and A063524 (1, 0, 0, 0, ...)} and its Dirichlet inverse.
The first negative term is a(5760) = -1223227750.

Links

Crossrefs

Cf. A000203, A001223, A001248, A003961, A063524, A341512, A347096.
Cf. also A346236, A346240, A347099.

Programs

  • PARI
    up_to = 16384;
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341512(n) = { my(u=A003961(n)); ((sigma(n)*u) - (n*sigma(u))); };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA341512(n));
v347096 = DirInverseCorrect(vector(up_to,n,Aux347096(n)));
A347096(n) = v347096[n];
A347097(n) = if(1==n,2,A341512(n) + A347096(n));

Formula

a(1) = 2, and for n>1, a(n) = -Sum_{d|n, 1A341512(d) * A347096(n/d).
For all n >= 1, a(A001248(n)) = A001223(n)^2.
Showing 1-4 of 4 results.

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