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 1-8 of 8 results.

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.

A280301 Numbers with 73 divisors.

Original entry on oeis.org

4722366482869645213696, 22528399544939174411840147874772641, 211758236813575084767080625169910490512847900390625, 7031676478883553279994550741476882515263791803223057265323201, 955593817727321453093807642925081991552428315714137911219172409259950196321
Offset: 1

Views

Author

Omar E. Pol, Dec 31 2016

Keywords

Comments

Also, 72nd 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 = 73.

Examples

			a(1) = 2^72, a(2) = 3^72, a(3) = 5^72, a(4) = 7^72, a(5) = 11^72.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280299, A280346, A280347, A280349, A261700.

Programs

  • Mathematica
    Array[Prime[#]^72 &, {5}] (* Michael De Vlieger, Dec 31 2016 *)
  • PARI
    a(n)=prime(n)^72

Formula

a(n) = A000040(n)^(73-1) = A000040(n)^72.
A000005(a(n)) = 73.

A280346 Numbers with 79 divisors.

Original entry on oeis.org

302231454903657293676544, 16423203268260658146231467800709255289, 3308722450212110699485634768279851414263248443603515625, 827269706064171159838078900184013751038269841857389464208009274449, 1692892739326831320764318961708001178036611459414853872137348292520966629744627081
Offset: 1

Views

Author

Omar E. Pol, Jan 01 2017

Keywords

Comments

Also, 78th 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 = 79.

Examples

			a(1) = 2^78, a(2) = 3^78, a(3) = 5^78, a(4) = 7^78, a(5) = 11^78.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280299, A280301, A280347, A280349, A261700.

Programs

  • Mathematica
    With[{p = 22}, Table[Prime[n]^(Prime@ p - 1), {n, 5}]] (* Michael De Vlieger, Jan 01 2017 *)
  • PARI
    a(n)=prime(n)^78

Formula

a(n) = A000040(n)^(79-1) = A000040(n)^78.
A000005(a(n)) = 79.

A280347 Numbers with 83 divisors.

Original entry on oeis.org

4835703278458516698824704, 1330279464729113309844748891857449678409, 2067951531382569187178521730174907133914530277252197265625, 1986274564260074954771227439341817016242885890299592103563430267952049, 24785642596484137367310393918366845247634028377292875541962916350799472426091085092921
Offset: 1

Views

Author

Omar E. Pol, Jan 01 2017

Keywords

Comments

Also, 82nd 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 = 83.

Examples

			a(1) = 2^82, a(2) = 3^82, a(3) = 5^82, a(4) = 7^82, a(5) = 11^82.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280299, A280301, A280346, A280349, A261700.

Programs

  • Mathematica
    With[{p = 23}, Table[Prime[n]^(Prime@ p - 1), {n, 5}]] (* Michael De Vlieger, Jan 01 2017 *)
  • PARI
    a(n)=prime(n)^82

Formula

a(n) = A000040(n)^(83-1) = A000040(n)^82.
A000005(a(n)) = 83.

A280349 Numbers with 89 divisors.

Original entry on oeis.org

309485009821345068724781056, 969773729787523602876821942164080815560161, 32311742677852643549664402033982923967414535582065582275390625, 233683216210633558353880137011125430143959282107856711392134007594290612801, 43909277783870034878569768760415886733743786946105343887995366053338664170638348798300219681
Offset: 1

Views

Author

Omar E. Pol, Jan 01 2017

Keywords

Comments

Also, 88th 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 = 89.

Examples

			a(1) = 2^88, a(2) = 3^88, a(3) = 5^88, a(4) = 7^88, a(5) = 11^88.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280299, A280301, A280346, A280347, A261700.

Programs

  • Mathematica
    With[{p = 24}, Table[Prime[n]^(Prime@ p - 1), {n, 5}]] (* Michael De Vlieger, Jan 01 2017 *)
  • PARI
    a(n)=prime(n)^88

Formula

a(n) = A000040(n)^(89-1) = A000040(n)^88.
A000005(a(n)) = 89.

A280350 Numbers with 97 divisors.

Original entry on oeis.org

79228162514264337593543950336, 6362685441135942358474828762538534230890216321, 12621774483536188886587657044524579674771302961744368076324462890625, 1347137238494276547832006567721872890819326613454654477690085519113574118965817601, 9412343651268540526001186511911506574868063110469548823950876000379062365652829504091329792873336961
Offset: 1

Views

Author

Omar E. Pol, Jan 02 2017

Keywords

Comments

Also, 96th 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 = 97.

Examples

			a(1) = 2^96, a(2) = 3^96, a(3) = 5^96, a(4) = 7^96, a(5) = 11^96.

Links

Crossrefs

Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280299, A280301, A280346, A280347, A280349, A261700.

Programs

  • Magma
    [NthPrime(n)^96: n in [1..5]]; // Vincenzo Librandi, Jan 06 2017
  • Mathematica
    With[{p = 25}, Table[Prime[n]^(Prime[p] - 1), {n, 5}]] (* Michael De Vlieger, Jan 02 2017 *)
  • PARI
    a(n)=prime(n)^96

Formula

a(n) = A000040(n)^(97-1) = A000040(n)^96.
A000005(a(n)) = 97.
Showing 1-8 of 8 results.

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