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 1-2 of 2 results.

A346239 Möbius transform of A341512, sigma(n)*A003961(n) - n*sigma(A003961(n)).

Original entry on oeis.org

0, 1, 2, 10, 2, 33, 4, 74, 44, 55, 2, 278, 4, 115, 116, 490, 2, 613, 4, 498, 242, 169, 6, 1942, 92, 265, 742, 1046, 2, 1591, 6, 3086, 344, 355, 330, 4986, 4, 487, 542, 3570, 2, 3347, 4, 1638, 2326, 737, 6, 12542, 376, 2121, 716, 2546, 6, 9869, 388, 7510, 986, 943, 2, 12894, 6, 1225, 4872, 18970, 630, 5353, 4, 3498, 1492
Offset: 1

Views

Author

Antti Karttunen, Jul 13 2021

Keywords

Links

Crossrefs

Cf. A000203, A003961, A008683, A341528, A341529, A341512, A346240, A347096, A347124, A347125.
Cf. also the sequences A001359, A029710, A031924 that give the positions of 2's, 4's and 6's in this sequence, or at least subsets of such positions.

Programs

Formula

a(n) = Sum_{d|n} A008683(n/d) * A341512(d).
a(n) = A341512(n) - A346240(n).
a(n) = A347125(n) - A347124(n). - Antti Karttunen, Aug 25 2021

A347124 Möbius transform of A341528, n * sigma(A003961(n)).

Original entry on oeis.org

1, 7, 17, 44, 39, 119, 83, 268, 261, 273, 153, 748, 233, 581, 663, 1616, 339, 1827, 455, 1716, 1411, 1071, 689, 4556, 1385, 1631, 3933, 3652, 927, 4641, 1177, 9712, 2601, 2373, 3237, 11484, 1553, 3185, 3961, 10452, 1803, 9877, 2063, 6732, 10179, 4823, 2537, 27472, 6433, 9695, 5763, 10252, 3179, 27531, 5967, 22244
Offset: 1

Views

Author

Antti Karttunen, Aug 24 2021

Keywords

Comments

Multiplicative because A341528 is.

Links

Crossrefs

Cf. A002117, A003961, A003973, A008683, A151800, A341528, A341512, A346239, A347125.

Programs

  • Mathematica
    f[p_, e_] := Module[{q = NextPrime[p]}, p^(e-1) * (q^e * (p*q-1) - p + 1)/(q-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 24 2023 *)
  • PARI
    A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A003973(n) = sigma(A003961(n));
A341528(n) = (n*A003973(n));
A347124(n) = sumdiv(n,d,moebius(n/d)*A341528(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A341528(d).
a(n) = A347125(n) - A346239(n).
Multiplicative with a(p^e) = p^(e-1)*(q^e*(p*q-1)-p+1)/(q-1), where q = A151800(p). - Sebastian Karlsson, Sep 02 2021
Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = (1/zeta(3)) / Product_{p prime} (1 - (q(p)-p)/p^2 - q(p)/p^3) = 5.6488805... , and q(p) = A151800(p). - Amiram Eldar, Dec 24 2023
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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