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.

A064086 Condensed version of A064085: all terms of A064085 with values greater than 1 (which coincides with all terms of A064085 with nonprime power index).

Original entry on oeis.org

3, 11, 39, 43, 151, 171, 2255, 2359, 683, 9399, 2731, 140911, 1649373, 599479, 43691, 8727391, 8965359, 174763, 9588151, 139090655, 1649061309, 572942063, 2221095391, 2796203, 613576119, 11184811, 2454285751, 36654862063, 44739243
Offset: 1

Views

Author

Jens Voß, Sep 04 2001

Keywords

Links

Crossrefs

Cf. A024619, A000225, A064084, A064085.

Formula

a(n) = A064085 (A024619(n)).

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003

A064084 A multiplicative version of 2^n - 1 (A000225).

Original entry on oeis.org

1, 3, 7, 15, 31, 21, 127, 255, 511, 93, 2047, 105, 8191, 381, 217, 65535, 131071, 1533, 524287, 465, 889, 6141, 8388607, 1785, 33554431, 24573, 134217727, 1905, 536870911, 651, 2147483647, 4294967295, 14329, 393213, 3937, 7665, 137438953471, 1572861, 57337
Offset: 1

Views

Author

Jens Voß, Sep 04 2001

Keywords

Comments

Since n -> 2^n - 1 is an embedding of the ordered structure N = {1, 2, 3, ...} (the order being the "divides" relation) into itself, a(n) always divides A000225(n); the sequence of quotients of A000225 and a is A064085.

Examples

			a(6) = (2^2 - 1) * (2^3 - 1) = 21 since 6 = 2 * 3.

Links

Crossrefs

Cf. A000225, A064085, A064086.

Programs

  • Maple
    a:= n-> mul(2^(i[1]^i[2])-1, i=ifactors(n)[2]):
seq(a(n), n=1..50);  # Alois P. Heinz, Jun 09 2014
  • Mathematica
    a[n_] := Times @@ (2^(Power @@@ FactorInteger[n]) - 1); Array[a, 40] (* Amiram Eldar, Aug 31 2023 *)
  • PARI
    a(n) = my(f=factor(n)); for (i=1, #f~, f[i,1] = 2^(f[i,1]^f[i,2])-1; f[i,2]=1); factorback(f); \\ Michel Marcus, Jun 09 2014

Formula

a(n) = (2^((p_1)^(e_1)) - 1) * ... * (2^((p_k)^(e_k)) - 1) where (p_1)^(e_1) * ... * (p_k)^(e_k) is the prime factorization of n.

Extensions

More terms from Michel Marcus, Jun 09 2014
Showing 1-2 of 2 results.

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