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.

A369741 a(n) = Sum_{p|n, p prime} p^Omega(n/p).

Original entry on oeis.org

0, 1, 1, 2, 1, 5, 1, 4, 3, 7, 1, 13, 1, 9, 8, 8, 1, 13, 1, 29, 10, 13, 1, 35, 5, 15, 9, 53, 1, 38, 1, 16, 14, 19, 12, 35, 1, 21, 16, 133, 1, 62, 1, 125, 34, 25, 1, 97, 7, 29, 20, 173, 1, 35, 16, 351, 22, 31, 1, 160, 1, 33, 58, 32, 18, 134, 1, 293, 26, 78, 1, 97, 1, 39
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 30 2024

Keywords

Links

Crossrefs

Cf. A001222 (Omega), A307409, A369909.
Cf. also A345301.

Programs

  • Mathematica
    Table[DivisorSum[n, #^PrimeOmega[n/#] &, PrimeQ[#] &], {n, 100}]
  • PARI
    A369741(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i,1]^bigomega(n/f[i, 1]))); \\ Antti Karttunen, Jan 23 2025

Formula

a(p^k) = p^(k-1), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

A369747 a(n) = Sum_{p|n, p prime} pi(n/p).

Original entry on oeis.org

0, 0, 0, 1, 0, 3, 0, 2, 2, 4, 0, 5, 0, 5, 5, 4, 0, 7, 0, 6, 6, 6, 0, 9, 3, 7, 4, 8, 0, 13, 0, 6, 7, 8, 7, 12, 0, 9, 8, 12, 0, 17, 0, 10, 10, 10, 0, 15, 4, 13, 9, 11, 0, 16, 8, 13, 10, 11, 0, 23, 0, 12, 12, 11, 9, 22, 0, 13, 11, 21, 0, 20, 0, 13, 15, 14, 9, 24, 0, 18, 9
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 30 2024

Keywords

Crossrefs

Cf. A000040, A000720 (pi), A062774, A345301, A369745.

Programs

  • Mathematica
    Table[DivisorSum[n, PrimePi[n/#] &, PrimeQ[#] &], {n, 100}]

Formula

a(p^k) = pi(p^(k-1)), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

A369868 a(n) = Sum_{p|n, p prime} n^pi(n/p).

Original entry on oeis.org

0, 1, 1, 4, 1, 42, 1, 64, 81, 1010, 1, 1872, 1, 38430, 3600, 65536, 1, 110808, 1, 160400, 194922, 5153654, 1, 8294400, 15625, 308915802, 531441, 481891088, 1, 729837000, 1, 1073741824, 39136482, 52523350178, 1543500, 78424630272, 1, 4347792138534, 3518745282
Offset: 1

Views

Author

Wesley Ivan Hurt, Feb 03 2024

Keywords

Crossrefs

Cf. A000720 (pi), A345301, A369745, A369747.

Programs

  • Mathematica
    Table[DivisorSum[n, n^PrimePi[n/#] &, PrimeQ[#] &], {n, 60}]

Formula

a(p^k) = p^(k*pi(p^(k-1))), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

A369869 a(n) = n * Sum_{p|n, p prime} pi(n/p) / p.

Original entry on oeis.org

0, 0, 0, 2, 0, 8, 0, 8, 6, 17, 0, 26, 0, 30, 21, 32, 0, 54, 0, 48, 34, 57, 0, 92, 15, 80, 36, 92, 0, 148, 0, 96, 61, 121, 43, 186, 0, 154, 84, 192, 0, 270, 0, 184, 126, 209, 0, 312, 28, 265, 125, 242, 0, 369, 70, 284, 158, 292, 0, 520, 0, 343, 204, 352, 93, 557, 0
Offset: 1

Views

Author

Wesley Ivan Hurt, Feb 03 2024

Keywords

Links

Crossrefs

Cf. A000720 (pi), A345301, A369745, A369747, A369868.

Programs

  • Mathematica
    Table[n*DivisorSum[n, PrimePi[n/#]/# &, PrimeQ[#] &], {n, 100}]
  • PARI
    A369869(n) = if(1==n, 0, n*my(f=factor(n)); n*sum(i=1, #f~, primepi(n/f[i, 1])/f[i, 1])); \\ Antti Karttunen, Jan 22 2025

Formula

a(p^k) = p^(k-1) * pi(p^(k-1)), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024
Showing 1-4 of 4 results.

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

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