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.

A348949 a(n) = A003959(A276086(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

Original entry on oeis.org

1, 3, 4, 12, 16, 48, 6, 18, 24, 72, 96, 288, 36, 108, 144, 432, 576, 1728, 216, 648, 864, 2592, 3456, 10368, 1296, 3888, 5184, 15552, 20736, 62208, 8, 24, 32, 96, 128, 384, 48, 144, 192, 576, 768, 2304, 288, 864, 1152, 3456, 4608, 13824, 1728, 5184, 6912, 20736, 27648, 82944, 10368, 31104, 41472, 124416, 165888, 497664, 64
Offset: 0

Views

Author

Antti Karttunen, Nov 07 2021

Keywords

Crossrefs

Programs

  • PARI
    A348949(n) = { my(m=1, p=2); while(n, m *= ((1+p)^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = A003959(A276086(n)).
a(n) = A276086(n) + A348950(n).

A348997 a(n) = A348733(A276086(n)), where A348733(n) = gcd(A003959(n), A034448(n)), and A276086 gives the prime product form of primorial base expansion of n.

Original entry on oeis.org

1, 3, 4, 12, 2, 6, 6, 18, 24, 72, 12, 36, 2, 6, 8, 24, 4, 12, 18, 54, 72, 216, 36, 108, 2, 6, 8, 24, 4, 12, 8, 24, 32, 96, 16, 48, 48, 144, 192, 576, 96, 288, 16, 48, 64, 192, 32, 96, 144, 432, 576, 1728, 288, 864, 16, 48, 64, 192, 32, 96, 2, 6, 8, 24, 4, 12, 12, 36, 48, 144, 24, 72, 4, 12, 16, 48, 8, 24, 36, 108, 144
Offset: 0

Views

Author

Antti Karttunen, Nov 07 2021

Keywords

Crossrefs

Cf. also A346471 for similar construction. (Compare the scatter plots).

Programs

  • PARI
    A348997(n) = { my(m1=1, m2=1, p=2); while(n, if(n%p, m1 *= ((1+p)^(n%p)); m2 *= (1+(p^(n%p)))); n = n\p; p = nextprime(1+p)); gcd(m1, m2); };

Formula

a(n) = A348733(A276086(n)) = gcd(A348949(n), A348996(n)).

A349000 a(n) = A323166(A276086(n)), where A323166(n) = gcd(n, usigma(n)), usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.

Original entry on oeis.org

1, 1, 1, 6, 1, 6, 1, 2, 3, 6, 15, 90, 1, 2, 1, 6, 5, 30, 1, 2, 3, 6, 45, 90, 1, 2, 1, 6, 5, 30, 1, 2, 1, 6, 1, 6, 1, 2, 3, 6, 15, 90, 1, 2, 1, 6, 5, 30, 7, 14, 21, 42, 315, 630, 1, 2, 1, 6, 5, 30, 1, 2, 1, 6, 1, 6, 5, 10, 15, 30, 15, 90, 25, 50, 25, 150, 25, 150, 175, 350, 525, 1050, 7875, 15750, 25, 50, 25, 150, 125, 750
Offset: 0

Views

Author

Antti Karttunen, Nov 07 2021

Keywords

Crossrefs

Programs

  • PARI
    A349000(n) = { my(m1=1, m2=1, p=2, u); while(n, if(n%p, u = p^(n%p); m1 *= u; m2 *= (1+u)); n = n\p; p = nextprime(1+p)); gcd(m1,m2); };

Formula

a(n) = A323166(A276086(n)) = gcd(A276086(n), A348996(n)).
Showing 1-3 of 3 results.