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 1-5 of 5 results.

A045968 a(1)=5; for n >= 2, if n = Product p_i^e_i, then a(n) = Product p_{i+3}^e_i.

Original entry on oeis.org

5, 7, 11, 49, 13, 77, 17, 343, 121, 91, 19, 539, 23, 119, 143, 2401, 29, 847, 31, 637, 187, 133, 37, 3773, 169, 161, 1331, 833, 41, 1001, 43, 16807, 209, 203, 221, 5929, 47, 217, 253, 4459, 53, 1309, 59, 931, 1573, 259, 61, 26411, 289, 1183, 319, 1127, 67, 9317, 247
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			If n = 9 = 3^2, then a(n) = 11^2 = 121 (since 11 is the third prime after 3).

References

Crossrefs

Cf. A045965, A045966, A045967, A045969, A045970, A045971, A045972, A045973.

Programs

  • Mathematica
    f[p_, e_] := NextPrime[p, 3]^e; a[1] = 5; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2023 *)

Extensions

More terms from David W. Wilson
Erroneous linear recurrence deleted by Harvey P. Dale, May 07 2018

A045970 a(1)=7; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+4}^e_i.

Original entry on oeis.org

7, 11, 13, 121, 17, 143, 19, 1331, 169, 187, 23, 1573, 29, 209, 221, 14641, 31, 1859, 37, 2057, 247, 253, 41, 17303, 289, 319, 2197, 2299, 43, 2431, 47, 161051, 299, 341, 323, 20449, 53, 407, 377, 22627, 59, 2717, 61, 2783, 2873, 451, 67, 190333, 361, 3179, 403
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

Crossrefs

Cf. A045965, A045966, A045967, A045968, A045969, A045971, A045972, A045973.

Programs

  • Mathematica
    f[p_, e_] := NextPrime[p, 4]^e; a[1] = 7; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2023 *)

Extensions

More terms from David W. Wilson

A045973 a(1)=10; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+1}^e_i * Product p_{i+3}^e_i.

Original entry on oeis.org

10, 21, 55, 441, 91, 1155, 187, 9261, 3025, 1911, 247, 24255, 391, 3927, 5005, 194481, 551, 63525, 713, 40131, 10285, 5187, 1073, 509355, 8281, 8211, 166375, 82467, 1271, 105105, 1591, 4084101, 13585, 11571, 17017, 1334025, 1927, 14973, 21505, 842751
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

Crossrefs

Cf. A045965, A045966, A045967, A045968, A045969, A045970, A045971, A045972.

Programs

  • Mathematica
    f[p_, e_] := NextPrime[p]^e * NextPrime[p, 3]^e; a[1] = 10; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2023 *)

Formula

Sum_{n>=1} 1/a(n) = -9/10 + Product_{k>=1} (1+1/(prime(k)*prime(k+4)-1)) = 0.2602421684... . - Amiram Eldar, Sep 19 2023

Extensions

More terms from David W. Wilson

A045969 a(1)=6; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+1}^e_i * Product p_{i+2}^e_i.

Original entry on oeis.org

6, 15, 35, 225, 77, 525, 143, 3375, 1225, 1155, 221, 7875, 323, 2145, 2695, 50625, 437, 18375, 667, 17325, 5005, 3315, 899, 118125, 5929, 4845, 42875, 32175, 1147, 40425, 1517, 759375, 7735, 6555, 11011, 275625, 1763, 10005, 11305, 259875, 2021, 75075
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

Crossrefs

Cf. A045965, A045966, A045967, A045968, A045970, A045971, A045972, A045973.

Programs

  • Mathematica
    f[p_, e_] := (NextPrime[p] * NextPrime[p, 2])^e; a[1] = 6; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2023 *)

Formula

Sum_{n>=1} 1/a(n) = -5/6 + Product_{k>=2} (1+1/(prime(k)*prime(k+1)-1)) = 0.31383788... . - Amiram Eldar, Sep 19 2023

Extensions

More terms from David W. Wilson

A045972 a(1)=9; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+2}^{e_i+1}.

Original entry on oeis.org

9, 25, 49, 125, 121, 1225, 169, 625, 343, 3025, 289, 6125, 361, 4225, 5929, 3125, 529, 8575, 841, 15125, 8281, 7225, 961, 30625, 1331, 9025, 2401, 21125, 1369, 148225, 1681, 15625, 14161, 13225, 20449, 42875, 1849, 21025, 17689, 75625, 2209, 207025
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

Crossrefs

Cf. A045965, A045966, A045967, A045968, A045969, A045970, A045971, A045973, A082695.

Programs

  • Mathematica
    f[p_, e_] := NextPrime[p, 2]^(e + 1); a[1] = 9; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2023 *)

Formula

Sum_{n>=1} 1/a(n) = (4/7) * (zeta(2)*zeta(3)/zeta(6)) - 8/9 = 0.221737646437... . - Amiram Eldar, Sep 19 2023

Extensions

More terms from David W. Wilson
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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