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.

A358219 Indices k where A358217(k) != A358218(k).

Original entry on oeis.org

15, 35, 45, 70, 75, 77, 105, 135, 140, 143, 154, 165, 175, 195, 221, 225, 231, 245, 255, 280, 285, 286, 308, 315, 323, 345, 350, 375, 385, 405, 429, 435, 437, 442, 450, 455, 462, 465, 490, 495, 525, 539, 555, 560, 572, 585, 595, 615, 616, 645, 646, 663, 665, 667, 675, 693, 700, 705, 715, 735, 765, 770, 795, 805
Offset: 1

Views

Author

Antti Karttunen, Nov 04 2022

Keywords

Links

Crossrefs

Cf. A319627, A328478, A358217, A358218.

A319627 Primorial deflation of n (denominator): Let f be the completely multiplicative function over the positive rational numbers defined by f(p) = A034386(p) for any prime number p; f constitutes a permutation of the positive rational numbers; let g be the inverse of f; for any n > 0, a(n) is the denominator of g(n).

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 5, 1, 4, 3, 7, 1, 11, 5, 2, 1, 13, 2, 17, 3, 10, 7, 19, 1, 9, 11, 8, 5, 23, 1, 29, 1, 14, 13, 3, 1, 31, 17, 22, 3, 37, 5, 41, 7, 4, 19, 43, 1, 25, 9, 26, 11, 47, 4, 21, 5, 34, 23, 53, 1, 59, 29, 20, 1, 33, 7, 61, 13, 38, 3, 67, 1, 71, 31, 6
Offset: 1

Views

Author

Rémy Sigrist, Sep 25 2018

Keywords

Comments

See A319626 for the corresponding numerators and additional comments.

Examples

			f(21/5) = (2*3) * (2*3*5*7) / (2*3*5) = 42, hence g(42) = 21/5 and a(42) = 5.

Links

Crossrefs

Cf. A025487 (positions of 1's), A064989, A329900, A358217 [= bigomega(a(n))].
Cf. A319626 (numerators, see comments there).
Cf. also A307035, A337377, A348990 [= a(A003961(n))], A349169 (odd numbers k such that A348993(k) = a(k)), A354365/A354366.

Programs

  • Mathematica
    Array[#2/GCD[#1, #2] & @@ {#, Apply[Times, Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#]]]} &, 120] (* Michael De Vlieger, Aug 27 2020 *)
  • PARI
    a(n) = my (f=factor(n)); denominator(prod(i=1, #f~, my (p=f[i,1]); (p/if (p>2, precprime(p-1), 1))^f[i,2]))

Formula

a(n) = A064989(n) / gcd(n, A064989(n)).
a(n) = 1 iff n belongs to A025487.

Extensions

"Primorial deflation" prefixed to the name by Antti Karttunen, Apr 29 2022

A358218 Number of prime factors (with multiplicity) in A328478(n).

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 3, 1, 1, 0, 1, 0, 2, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 0, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 0, 1, 1, 3, 0, 2, 1, 1, 1, 2, 2, 1, 0, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 0, 1, 2, 3, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 2, 0
Offset: 1

Views

Author

Antti Karttunen, Nov 04 2022

Keywords

Links

Crossrefs

Cf. A001222, A025487 (positions of zeros), A328478, A355930.
Cf. A358219 (positions where differs from A358217).

Programs

Formula

a(n) = A001222(A328478(n)).
a(n) <= A355930(n).
Apparently, a(n) >= A358217(n) for all n.
Showing 1-3 of 3 results.

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