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.

User: Bhupendra Kumar Singh

Bhupendra Kumar Singh's wiki page.

Bhupendra Kumar Singh has authored 4 sequences.

A345250 a(n) is the number of divisors of A344422(n).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 18, 28, 36, 42, 48, 72, 96, 108, 128, 144, 168, 192, 336, 384, 448, 504, 672, 896, 960, 1008, 1134, 1296, 1344, 2560, 2592, 3456, 3584, 4320, 4608, 5376, 6144, 6336, 6912, 9216, 10240, 12288, 13824, 15360, 16128, 16384, 20736, 23328, 24576
Offset: 1

Views

Author

Bhupendra Kumar Singh, Jun 12 2021

Keywords

Comments

Sequence proposed by Felix Fröhlich in the first comment of A344422.

Links

Crossrefs

Records in A076888.
Cf. A000005, A002113, A002182, A344422.

Formula

a(n) = A000005(A344422(n)).

A345260 a(n) = A000203(A344422(n)).

Original entry on oeis.org

1, 3, 7, 12, 84, 144, 728, 6096, 8736, 19812, 85120, 163520, 738720, 871416, 2419200, 2935296, 7567168, 15193920, 84319872, 169303680, 259445760, 934545248, 8600626944, 9438363648, 19853729280, 34805721600, 87037870374, 165451302016, 254879514624, 957538713600
Offset: 1

Views

Author

Bhupendra Kumar Singh, Jun 12 2021

Keywords

Links

Crossrefs

Cf. A000203, A344422.

A344436 Numbers k such that k, 2*k, 3*k, 4*k, 5*k and 6*k are anagrams and no digit of k is zero.

Original entry on oeis.org

142857, 1429857, 14299857, 142999857, 1429999857, 14299999857, 142857142857, 142999999857, 1428571429857, 1429857142857, 1429999999857, 14285714299857, 14298571429857, 14299857142857, 14299999999857, 137428291864557, 137464282918557, 142829186455737
Offset: 1

Views

Author

Bhupendra Kumar Singh, May 19 2021

Keywords

Comments

All terms are divisible by 9.
a(1) = 143*999 = 1287*111;
a(2) = 143*9999 = 1287*1111;
a(7) = 143*999000999 = 1287*111000111; etc.
a(n) = k is odd. Proof: If k is even then 5*k ends in 0, which is forbidden by definition. - David A. Corneth, May 22 2021

Examples

			142857, 1429857, and 14299857 are in the sequence:
.
      k        2*k       3*k       4*k       5*k       6*k
  --------  --------  --------  --------  --------  --------
    142857    285714    428571    571428    714285    857142
   1429857   2859714   4289571   5719428   7149285   8579142
  14299857  28599714  42899571  57199428  71499285  85799142

Crossrefs

Cf. A023086, A245682, A323711.

Programs

  • PARI
    isok(k) = {my(d = vecsort(digits(k))); vecmin(d) && (d==vecsort(digits(2*k))) && (d==vecsort(digits(3*k))) && (d==vecsort(digits(4*k))) && (d==vecsort(digits(5*k))) && (d==vecsort(digits(6*k)));} \\ Michel Marcus, Jun 01 2021

Extensions

Data corrected by David A. Corneth, May 22 2021

A344422 Palindromes having more divisors than all smaller palindromes.

Original entry on oeis.org

1, 2, 4, 6, 44, 66, 252, 2112, 2772, 6336, 27972, 48384, 219912, 252252, 696696, 828828, 2114112, 4228224, 21333312, 42666624, 63999936, 234666432, 2154664512, 2329559232, 4815995184, 8402442048, 21354645312, 40362626304, 63708380736, 211887788112
Offset: 1

Views

Author

Bhupendra Kumar Singh, May 17 2021

Keywords

Comments

A000005(a(n)) = 1, 2, 3, 4, 6, 8, 18, 28, 36, 42, 48, 72, 96, 108, 128, 144, 168, 192, 336, 384, .... - Felix Fröhlich, May 19 2021
From Jon E. Schoenfield, Jun 22 2021: (Start)
There exists at least one m-digit term for every m in 1..22 except 21 (see the b-file).
Conjecture: all terms after a(1)=1 are even. (End)

Examples

			Terms include: 4 (3 divisors); 6 (4 divisors); 44 (6 divisors); 66 (8 divisors); 252 (18 divisors).

Links

Crossrefs

Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A002182, A084324, A093036, A345250.

Programs

  • Mathematica
    pal=Union@Flatten[Table[r=IntegerDigits@n;FromDigits/@(Join[r,#]&/@{Reverse@r,Rest@Reverse@r}),{n,10^5}]];m=0;lst={};Do[s=DivisorSigma[0,k];If[s>m,AppendTo[lst,k];m=s],{k,pal}];lst (* Giorgos Kalogeropoulos, Dec 08 2021 *)
  • PARI
    \\ See PARI link. David A. Corneth, May 18 2021

Formula

A000005(a(n)) = A345250(n).

Extensions

Data corrected and extended by David A. Corneth, May 18 2021

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