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.

A068511 (Product of primes <= n) - 2^(n-1).

Original entry on oeis.org

0, 0, 2, -2, 14, -2, 146, 82, -46, -302, 1286, 262, 25934, 21838, 13646, -2738, 444974, 379438, 9437546, 9175402, 8651114, 7602538, 218898566, 214704262, 206315654, 189538438, 155984006, 88875142, 6201257774, 5932822318, 199486748306, 198413006482, 196265522834, 191970555538
Offset: 1

Views

Author

N. J. A. Sloane, Mar 21 2002

Keywords

Crossrefs

Cf. A059794, A068511.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 21 2002

A067068 a(n) = n* - 2^n, where n* (A003418) = least common multiple of the numbers [1,...,n].

Original entry on oeis.org

-1, -2, -2, -4, 28, -4, 292, 584, 2008, 1496, 25672, 23624, 352168, 343976, 327592, 655184, 12121168, 11990096, 232268272, 231743984, 230695408, 228598256, 5345840272, 5337451664, 26737589968, 26704035536, 80179215472, 80044997744
Offset: 1

Views

Author

N. J. A. Sloane, Feb 17 2002

Keywords

Comments

It is known that this sequence is nonnegative for n >= 7. This can be established using the methods used to show A059794 is nonnegative. - Carl Pomerance, Bell Labs, Feb 16 2002

References

  • Tenenbaum, G. (2015). Introduction to analytic and probabilistic number theory, 3rd ed., American Mathematical Soc. See Theorem 1.5.

Links

Crossrefs

Cf. A003418, A059794.

Programs

  • Mathematica
    Table[LCM@@Range[n]-2^n,{n,30}] (* Harvey P. Dale, Sep 24 2022 *)

A068510 a(n) = lcm(1,...,n) - (product of primes <= n).

Original entry on oeis.org

0, 0, 0, 6, 30, 30, 210, 630, 2310, 2310, 25410, 25410, 330330, 330330, 330330, 690690, 11741730, 11741730, 223092870, 223092870, 223092870, 223092870, 5131136010, 5131136010, 26548051530, 26548051530, 80090340330, 80090340330
Offset: 1

Views

Author

N. J. A. Sloane, Mar 21 2002

Keywords

References

  • Tenenbaum, G. (2015). Introduction to analytic and probabilistic number theory, 3rd ed., American Mathematical Soc. See page 22.

Links

Crossrefs

Cf. A059794, A068511.

Programs

  • Maple
    a[1] := 0:a[2] := 0:l := 2:p := 3:pp := 2:for i from 3 to 50 do l := ilcm(l,i): if(p=i) then pp := pp*p:p := nextprime(p):end if: a[i] := l-pp:end do:q := seq(a[j],j=1..50);
  • Mathematica
    f[n_] := (LCM @@ Table[i, {i, n}] - Product[Prime[i], {i, PrimePi[n]}]); Table[f[n], {n, 30}]

Extensions

More terms from Sascha Kurz, Mar 23 2002
Showing 1-3 of 3 results.

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

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