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 18 results. Next

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.

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.

A280298 Numbers with 67 divisors.

Original entry on oeis.org

73786976294838206464, 30903154382632612361920641803529, 13552527156068805425093160010874271392822265625, 59768263894155949306790119265585619217025149412430681649, 539407797827634189900210968137750826278309533633974732577186113975161
Offset: 1

Views

Author

Omar E. Pol, Dec 31 2016

Keywords

Comments

Also, 66th powers of primes.
More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 67.

Examples

			a(1) = 2^66, a(2) = 3^66, a(3) = 5^66, a(4) = 7^66, a(5) = 11^66.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280299, A280301, A261700.

Programs

  • Mathematica
    Array[Prime[#]^66 &, {5}] (* Michael De Vlieger, Dec 31 2016 *)
  • PARI
    a(n)=prime(n)^66

Formula

a(n) = A000040(n)^(67-1) = A000040(n)^66.
A000005(a(n)) = 67.

A280299 Numbers with 71 divisors.

Original entry on oeis.org

1180591620717411303424, 2503155504993241601315571986085849, 8470329472543003390683225006796419620513916015625, 143503601609868434285603076356671071740077383739246066639249, 7897469567994392174328988784504809847540729881935024059662581894710332201
Offset: 1

Views

Author

Omar E. Pol, Dec 31 2016

Keywords

Comments

Also, 70th powers of primes.
More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 71.

Examples

			a(1) = 2^70, a(2) = 3^70, a(3) = 5^70, a(4) = 7^70, a(5) = 11^70.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280301, A261700.

Programs

  • Mathematica
    Array[Prime[#]^70 &, {5}] (* Michael De Vlieger, Dec 31 2016 *)
  • PARI
    a(n)=prime(n)^70

Formula

a(n) = A000040(n)^(71-1) = A000040(n)^70.
A000005(a(n)) = 71.
Showing 1-10 of 18 results. Next

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

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