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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.

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A343886 a(n) = k/A097621(k) for k=A344826(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 5, 3, 5, 4, 8, 5, 5, 5, 4, 7, 8, 9, 12, 7, 6, 8, 12, 13, 14, 9, 16, 9, 12, 18, 12, 11, 21, 18, 12, 24, 7, 13, 14, 14, 15, 27, 17, 27, 20, 18, 33, 12, 11, 21, 32, 21, 20, 11, 22, 23, 21, 14, 28, 27, 24, 17
Offset: 1

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Author

Michel Marcus, Jun 03 2021

Keywords

Comments

A344826 is the sequence of numbers k such that k/A097621(k) is an integer. The current sequence lists the corresponding integer quotients.

Examples

			The first 12 terms of A344826 are (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), fixed points of A097621, for which k/A097621(k) is 1.
A344826(13) is 891, so a(13) = 891/A097621(891) = 891/297 = 3, so a(13) = 3.

Links

Crossrefs

Cf. A097621, A344826.

Programs

A095874 a(n) = k if n = A000961(k) (powers of primes), a(n) = 0 if n is not in A000961.

Original entry on oeis.org

1, 2, 3, 4, 5, 0, 6, 7, 8, 0, 9, 0, 10, 0, 0, 11, 12, 0, 13, 0, 0, 0, 14, 0, 15, 0, 16, 0, 17, 0, 18, 19, 0, 0, 0, 0, 20, 0, 0, 0, 21, 0, 22, 0, 0, 0, 23, 0, 24, 0, 0, 0, 25, 0, 0, 0, 0, 0, 26, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 0, 30, 0, 31, 0, 0, 0, 0, 0, 32, 0, 33, 0, 34, 0, 0, 0, 0, 0, 35, 0
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2004

Keywords

Comments

The name has been edited to clarify that the indices k refer to A000961 ("powers of primes" = {1} U A246655) and not to the list A246655 of proper prime powers. - M. F. Hasler, Jun 16 2021

Links

Crossrefs

Cf. A000961 (right inverse), A049084, A097621.

Programs

  • Haskell
    a095874 n | y == n    = length xs + 1
          | otherwise = 0
          where (xs, y:ys) = span (< n) a000961_list
-- Reinhard Zumkeller, Feb 16 2012, Jun 26 2011
  • Mathematica
    Join[{1},Module[{k=2},Table[If[PrimePowerQ[n],k;k++,0],{n,2,100}]]] (* Harvey P. Dale, Aug 15 2020 *)
  • PARI
    a(n)=if(isprimepower(n), sum(i=1,logint(n,2), primepi(sqrtnint(n,i)))+1, n==1) \\ Charles R Greathouse IV, Apr 29 2015
  • PARI
    {M95874=Map(); A095874(n,k)=if(mapisdefined(M95874,n,&k),k, isprimepower(n), mapput(M95874,n, k=sum(i=1,exponent(n), primepi(sqrtnint(n,i)))+1); k,n==1)} \\ Variant with memoization, possibly useful to compute A097621, A344826 and related. One may omit "isprimepower(n)," (possibly requiring factorization) and ",n==1" if n is known to be a power of a prime, i.e., to get a left inverse for A000961. - M. F. Hasler, Jun 15 2021
  • Python
    from sympy import primepi, integer_nthroot, primefactors
def A095874(n): return 1+int(primepi(n)+sum(primepi(integer_nthroot(n,k)[0]) for k in range(2,n.bit_length()))) if n==1 or len(primefactors(n))==1 else 0 # Chai Wah Wu, Jan 19 2025

Formula

a(n) = Sum_{1 <= k <= n} A010055(k); [corrected by M. F. Hasler, Jun 15 2021]
a(n) = A065515(n)*(A065515(n)-A065515(n-1)).
a(n) = A065515(n)*A069513(n). - M. F. Hasler, Jun 16 2021

Extensions

Edited by M. F. Hasler, Jun 15 2021
Showing 1-2 of 2 results.

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