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 1-10 of 19 results. Next

A139572 Numbers with 37 divisors.

Original entry on oeis.org

68719476736, 150094635296999121, 14551915228366851806640625, 2651730845859653471779023381601, 30912680532870672635673352936887453361, 12646218552730347184269489080961456410641
Offset: 1

Views

Author

Omar E. Pol, May 07 2008

Keywords

Comments

36th powers of primes. The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139573.

Programs

Formula

a(n) = A000040(n)^(37-1) = A000040(n)^36.

Extensions

More terms from R. J. Mathar, Feb 05 2010

A139574 Numbers with 43 divisors.

Original entry on oeis.org

4398046511104, 109418989131512359209, 227373675443232059478759765625, 311973482284542371301330321821976049, 54763699237492901685126120802225273763666521, 61040881526285814362156628321386486455989674569
Offset: 1

Views

Author

Omar E. Pol, May 09 2008

Keywords

Comments

42nd powers of primes. The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139575.

Programs

Formula

a(n)=A000040(n)^(43-1)=A000040(n)^42.

Extensions

More terms from R. J. Mathar, May 11 2008

A139573 Numbers with 41 divisors.

Original entry on oeis.org

1099511627776, 12157665459056928801, 9094947017729282379150390625, 6366805760909027985741435139224001, 452592555681759518058893560348969204658401
Offset: 1

Views

Author

Omar E. Pol, May 07 2008

Keywords

Comments

40th powers of primes. The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572.

Programs

Formula

a(n)=A000040(n)^(41-1)=A000040(n)^40.

Extensions

More terms from Jon E. Schoenfield, May 18 2010

A139575 Numbers with 47 divisors.

Original entry on oeis.org

70368744177664, 8862938119652501095929, 142108547152020037174224853515625, 749048330965186233494494102694564493649, 801795320536133573571931534665380233173841533961
Offset: 1

Views

Author

Omar E. Pol, May 09 2008

Keywords

Comments

46th powers of primes. The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574.

Programs

Formula

a(n)=A000040(n)^(47-1)=A000040(n)^46.

Extensions

More terms from R. J. Mathar, May 11 2008

A173533 Numbers with 53 divisors.

Original entry on oeis.org

4503599627370496, 6461081889226673298932241, 2220446049250313080847263336181640625, 88124787089723195184393736687912818113311201, 1420429319844313329730664601483335671261683881745483121, 8415003868347247618489696679505181495471801448798649088081
Offset: 1

Views

Author

Omar E. Pol, Oct 16 2010

Keywords

Comments

52nd powers of primes.
The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575.

Programs

Formula

a(n) = A000040(n)^(53-1) = A000040(n)^52.

A183062 Numbers with 59 divisors.

Original entry on oeis.org

288230376151711744, 4710128697246244834921603689, 34694469519536141888238489627838134765625, 10367793076318844190248738727596255138212949486449
Offset: 1

Views

Author

Omar E. Pol, Jul 31 2011

Keywords

Comments

Also, 58th powers of primes.
The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533.

Programs

Formula

a(n) = A000040(n)^(59-1) = A000040(n)^58.
A000005(a(n)) = 59.

A183085 Numbers with 61 divisors.

Original entry on oeis.org

1152921504606846976, 42391158275216203514294433201, 867361737988403547205962240695953369140625, 508021860739623365322188197652216501772434524836001
Offset: 1

Views

Author

Omar E. Pol, Jul 31 2011

Keywords

Comments

Also, 60th powers of primes.
The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062.

Programs

  • PARI
    a(n)=prime(n)^60

Formula

a(n) = A000040(n)^(61-1) = A000040(n)^60.
A000005(a(n)) = 61.

A137493 Numbers with 30 divisors.

Original entry on oeis.org

720, 1008, 1200, 1584, 1620, 1872, 2268, 2352, 2448, 2592, 2736, 2800, 3312, 3564, 3888, 3920, 4050, 4176, 4212, 4400, 4464, 4608, 5200, 5328, 5508, 5808, 5904, 6156, 6192, 6768, 6800, 7452, 7500, 7600, 7632, 7938, 8112, 8496, 8624, 8784, 9200, 9396
Offset: 1

Views

Author

R. J. Mathar, Apr 22 2008

Keywords

Comments

Maple implementation: see A030513.
Numbers of the form p^29 (subset of A122970), p*q^2*r^4 (A179669), p^4*q^5 (A179702), p^2*q^9 (like 4608) or p*q^14, where p, q and r are distinct primes. - R. J. Mathar, Mar 01 2010

Links

Crossrefs

Cf. A137492 (29 divs), A139571 (31 divs).

Programs

  • Mathematica
    Select[Range[10000],DivisorSigma[0,#]==30&]  (* Harvey P. Dale, Feb 18 2011 *)
  • PARI
    is(n)=numdiv(n)==30 \\ Charles R Greathouse IV, Jun 19 2016
  • PARI
    list(lim)=
{
  my(f=(v,s)->concat(v,listsig(lim,s,1)));
  Set(fold(f, [[], [29], [5, 4], [9, 2], [14, 1], [4, 2, 1]]));
}
listsig(lim, sig, coprime)=
{
  my(e=sig[1]);
  if(#sig<2,
    if(#sig==0 || sig[1]==0, return(if(lim<1,[],[1])));
    my(P=primes([2,sqrtnint(lim\1,e)]));
    if(coprime==1, return(if(e>1,apply(p->p^e,P),P)));
    P=select(p->gcd(p,coprime)==1, P);
    if(e>1, P=apply(p->p^e, P));
    return(P);
  );
  my(v=List(),ss=sig[2..#sig],t=leastOfSig(ss));
  forprime(p=2,sqrtnint(lim\t,e),
    if(coprime%p,
        my(u=listsig(lim\p^e,ss,coprime*p));
        for(i=1,#u, listput(v,p^e*u[i]));
    )
  );
  Vec(v);
} \\ Charles R Greathouse IV, Nov 18 2021

Formula

A000005(a(n))=30.

A261700 Numbers with 101 divisors.

Original entry on oeis.org

1267650600228229401496703205376, 515377520732011331036461129765621272702107522001, 7888609052210118054117285652827862296732064351090230047702789306640625, 3234476509624757991344647769100216810857203198904625400933895331391691459636928060001
Offset: 1

Views

Author

Omar E. Pol, Aug 28 2015

Keywords

Comments

Also, 100th powers of primes.
The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Examples

			a(1) = 2^100, a(2) = 3^100, a(3) = 5^100, a(4) = 7^100.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085.

Programs

Formula

a(n) = A000040(n)^(101-1) = A000040(n)^100.
A000005(a(n)) = 101.

A319075 Square array T(n,k) read by antidiagonal upwards in which row n lists the n-th powers of primes, hence column k lists the powers of the k-th prime, n >= 0, k >= 1.

Original entry on oeis.org

1, 2, 1, 4, 3, 1, 8, 9, 5, 1, 16, 27, 25, 7, 1, 32, 81, 125, 49, 11, 1, 64, 243, 625, 343, 121, 13, 1, 128, 729, 3125, 2401, 1331, 169, 17, 1, 256, 2187, 15625, 16807, 14641, 2197, 289, 19, 1, 512, 6561, 78125, 117649, 161051, 28561, 4913, 361, 23, 1, 1024, 19683, 390625, 823543, 1771561, 371293
Offset: 0

Views

Author

Omar E. Pol, Sep 09 2018

Keywords

Comments

If n = p - 1 where p is prime, then row n lists the numbers with p divisors.
The partial sums of column k give the column k of A319076.

Examples

			The corner of the square array is as follows:
         A000079 A000244 A000351  A000420    A001020    A001022     A001026
A000012        1,      1,      1,       1,         1,         1,          1, ...
A000040        2,      3,      5,       7,        11,        13,         17, ...
A001248        4,      9,     25,      49,       121,       169,        289, ...
A030078        8,     27,    125,     343,      1331,      2197,       4913, ...
A030514       16,     81,    625,    2401,     14641,     28561,      83521, ...
A050997       32,    243,   3125,   16807,    161051,    371293,    1419857, ...
A030516       64,    729,  15625,  117649,   1771561,   4826809,   24137569, ...
A092759      128,   2187,  78125,  823543,  19487171,  62748517,  410338673, ...
A179645      256,   6561, 390625, 5764801, 214358881, 815730721, 6975757441, ...
...

Crossrefs

Rows 0-13: A000012, A000040, A001248, A030078, A030514, A050997, A030516, A092759, A179645, A179665, A030629, A079395, A030631, A138031.
Other rows n: A030635 (n=16), A030637 (n=18), A137486 (n=22), A137492 (n=28), A139571 (n=30), A139572 (n=36), A139573 (n=40), A139574 (n=42), A139575 (n=46), A173533 (n=52), A183062 (n=58), A183085 (n=60), A261700 (n=100).
Columns 1-15: A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.
Main diagonal gives A093360.
Second diagonal gives A062457.
Third diagonal gives A197987.
Removing the 1's we have A182944/ A182945.
Cf. A006093, A319074, A319076.

Programs

  • PARI
    T(n, k) = prime(k)^n;

Formula

T(n,k) = A000040(k)^n, n >= 0, k >= 1.
Showing 1-10 of 19 results. Next

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

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