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.

A158315 A158280(n)/7.

Original entry on oeis.org

1, 3, 3, 3, 6, 3, 3, 9, 3, 3, 9, 3, 6, 10, 3, 3, 9, 9, 3, 9, 3, 3, 18, 3, 6, 9, 3, 9, 9, 3, 3, 18, 9, 3, 9, 3, 3, 18, 9, 3, 15, 3, 9, 9, 3, 9, 9, 9, 3, 18, 3, 3, 27, 3, 3, 9, 3, 9, 18, 9, 6, 9, 10, 3, 9, 3, 9, 30, 3, 3, 9, 9, 9, 18, 3, 3, 18, 9, 3, 9, 9, 3, 27, 3, 6, 18, 3, 18, 9, 3, 3, 9, 9, 9, 30, 3, 3, 27
Offset: 0

Views

Author

Paul Curtz, Mar 16 2009

Keywords

Comments

A kind of core or backbone of A145511, A145501 and A145444.

Extensions

Edited and extended by R. J. Mathar, Apr 04 2009

A278223 Least number with the same prime signature as the n-th odd number: a(n) = A046523(2n-1).

Original entry on oeis.org

1, 2, 2, 2, 4, 2, 2, 6, 2, 2, 6, 2, 4, 8, 2, 2, 6, 6, 2, 6, 2, 2, 12, 2, 4, 6, 2, 6, 6, 2, 2, 12, 6, 2, 6, 2, 2, 12, 6, 2, 16, 2, 6, 6, 2, 6, 6, 6, 2, 12, 2, 2, 30, 2, 2, 6, 2, 6, 12, 6, 4, 6, 8, 2, 6, 2, 6, 24, 2, 2, 6, 6, 6, 12, 2, 2, 12, 6, 2, 6, 6, 2, 30, 2, 4, 12, 2, 12, 6, 2, 2, 6, 6, 6, 24, 2, 2, 30, 2, 2, 6, 6, 6, 12, 6, 2, 6, 6, 6, 6, 6, 2, 36, 2, 2
Offset: 1

Views

Author

Antti Karttunen, Nov 16 2016

Keywords

Comments

This sequence works as a filter for sequences related to the prime factorization of odd numbers by matching to any sequence that is obtained as f(2*n - 1), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ..."). The last line in Crossrefs section lists such sequences that were present in the database as of Nov 11 2016, although some of the matches might be spurious.

Links

Crossrefs

Odd bisection of A046523.
Cf. A064216, A244153, A245611, A278222, A278224, A278531.
Sequences that partition or seem to partition N into same or coarser equivalence classes: A099774, A100007, A193773, A101871, A158280, A158315, A158647, A285716.

Programs

  • Mathematica
    a[n_] := Times @@ (Prime[Range[Length[f = FactorInteger[2*n - 1]]]]^Sort[f[[;; , 2]], Greater]); a[1] = 1; Array[a, 100] (* Amiram Eldar, Jul 23 2023 *)
  • Python
    from sympy import factorint
def P(n):
    f = factorint(n)
    return sorted([f[i] for i in f])
def a046523(n):
    x=1
    while True:
        if P(n) == P(x): return x
        else: x+=1
def a(n): return a046523(2*n - 1) # Indranil Ghosh, May 11 2017
  • Python
    from math import prod
from sympy import prime, factorint
def A278223(n): return prod(prime(i+1)**e for i,e in enumerate(sorted(factorint((n<<1)-1).values(),reverse=True))) # Chai Wah Wu, Sep 16 2022
  • Scheme
    (define (A278223 n) (A046523 (+ n n -1)))
(define (A278223 n) (A046523 (A064216 n)))

Formula

a(n) = A046523(2n - 1).
a(n) = A046523(A064216(n)).
From Antti Karttunen, May 31 2017: (Start)
a(n) = A278222(A244153(n)).
a(n) = A278531(A245611(n)).
(End)

A158647 A145501(16n+8).

Original entry on oeis.org

13, 39, 39, 39, 78, 39, 39, 117, 39, 39, 117, 39, 78, 130, 39, 39, 117, 117, 39, 117, 39, 39, 234, 39, 78, 117, 39, 117, 117, 39, 39, 234, 117, 39, 117, 39, 39, 234, 117, 39, 195, 39, 117, 117, 39, 117, 117, 117, 39, 234, 39, 39, 351, 39, 39, 117, 39, 117, 234, 117, 78, 117, 130
Offset: 0

Views

Author

Paul Curtz, Mar 23 2009

Keywords

Comments

Apparently this is the same as 13*A158315(n).

Crossrefs

Cf. A158280, A145511, A145444.

Extensions

Edited and extended by R. J. Mathar, Apr 04 2009
Showing 1-3 of 3 results.

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