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.

A328771 Minimal number of primorials (A002110) that add to A328768(n), where A328768 is the first primorial based variant of arithmetic derivative.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 2, 5, 1, 4, 1, 4, 6, 2, 1, 3, 1, 4, 6, 6, 1, 6, 2, 5, 5, 10, 1, 6, 1, 6, 8, 7, 8, 6, 1, 6, 8, 6, 1, 5, 1, 8, 7, 8, 1, 6, 2, 9, 6, 10, 1, 8, 8, 8, 6, 9, 1, 10, 1, 4, 9, 8, 10, 13, 1, 8, 8, 14, 1, 10, 1, 5, 5, 10, 12, 10, 1, 6, 2, 7, 1, 8, 10, 6, 10, 14, 1, 5, 14, 8, 6, 8, 12, 6, 1, 9, 15, 8, 1, 16, 1, 14, 7
Offset: 0

Views

Author

Antti Karttunen, Oct 28 2019

Keywords

Links

Crossrefs

Cf. A002110, A276150, A324888, A328768, A328772.

Programs

  • PARI
    A002110(n) = prod(i=1,n,prime(i));
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A328771(n) = A276150(A328768(n));

Formula

a(n) = A276150(A328768(n)).

A328769 The second primorial based variant of arithmetic derivative: a(p) = A034386(p) for p prime, a(u*v) = a(u)*v + u*a(v), with a(0) = a(1) = 0.

Original entry on oeis.org

0, 0, 2, 6, 8, 30, 18, 210, 24, 36, 70, 2310, 48, 30030, 434, 120, 64, 510510, 90, 9699690, 160, 672, 4642, 223092870, 120, 300, 60086, 162, 896, 6469693230, 270, 200560490130, 160, 6996, 1021054, 1260, 216, 7420738134810, 19399418, 90168, 360, 304250263527210, 1386, 13082761331670030, 9328, 450, 446185786, 614889782588491410, 288, 2940, 650, 1531632
Offset: 0

Views

Author

Antti Karttunen, Oct 28 2019

Keywords

Links

Crossrefs

Cf. A002110, A034386, A108951, A328772.
Cf. also A003415, A258851, A328768, A328845, A328846.

Programs

  • PARI
    A034386(n) = factorback(primes(primepi(n)));
A328769(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A034386(f[i,1])/f[i, 1]));
  • PARI
    A002110(n) = prod(i=1,n,prime(i));
A328769(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1]))/f[i, 1]));

Formula

a(n) = n * Sum e_j * (p_j)#/p_j for n = Product p_j^e_j with (p_j)# = A034386(p_j).
A276150(a(n)) = A328772(n).
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.