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: Bhushan Bade

Bhushan Bade's wiki page.

Bhushan Bade has authored 5 sequences.

A277065 Sum of cubes of the digits of all divisors of n.

Original entry on oeis.org

1, 9, 28, 73, 126, 252, 344, 585, 757, 135, 3, 325, 29, 417, 279, 802, 345, 1494, 731, 207, 380, 27, 36, 909, 259, 261, 1108, 1001, 738, 531, 29, 837, 84, 444, 621, 1810, 371, 1278, 812, 783, 66, 741, 92, 219, 1197, 324, 408, 1702, 1137, 393, 498, 458, 153, 2034, 378, 1854, 1226, 1383, 855, 828
Offset: 1

Views

Author

Bhushan Bade, Sep 27 2016

Keywords

Examples

			For n = 10 the divisors of 10 are 1, 2, 5, 10, so a(10) = 1^3 + 2^3 + 5^3 + 1^3 + 0^3 = 1 + 8 + 125 + 1 + 0 = 135.
For n = 11 the divisors of 11 are 1, 11, so a(11) = 1^3 + 1^3 + 1^3 = 1 + 1 + 1 = 3.

Crossrefs

Cf. A055012, A276959.

Programs

  • Mathematica
    Table[Total[Flatten@ IntegerDigits[Divisors@ n]^3], {n, 60}] (* Michael De Vlieger, Sep 27 2016 *)
  • PARI
    a(n) = sumdiv(n, d, dd = digits(d); sum(k=1, #dd, dd[k]^3)); \\ Michel Marcus, Sep 29 2016

Extensions

More terms from Michael De Vlieger, Sep 27 2016

A276963 a(n) = prime(n+1)^4 - prime(n)^4.

Original entry on oeis.org

65, 544, 1776, 12240, 13920, 54960, 46800, 149520, 427440, 216240, 950640, 951600, 593040, 1460880, 3010800, 4226880, 1728480, 6305280, 5260560, 2986560, 10551840, 8508240, 15283920, 25787040, 15531120, 8490480, 18528720, 10078560, 21889200, 97097280, 34355280, 57775440
Offset: 1

Views

Author

Bhushan Bade, Sep 22 2016

Keywords

Examples

			a(1) = 3^4 - 2^4 = 65.
a(2) = 5^4 - 3^4 = 544.

Crossrefs

Cf. A069482, A129701.

A276959 Sum of squares of digits in all divisors of n.

Original entry on oeis.org

1, 5, 10, 21, 26, 50, 50, 85, 91, 31, 3, 71, 11, 71, 61, 122, 51, 196, 83, 51, 64, 15, 14, 155, 55, 55, 144, 155, 86, 111, 11, 135, 30, 80, 109, 262, 59, 160, 110, 131, 18, 141, 26, 63, 183, 70, 66, 272, 147, 85, 86, 100, 35, 290, 78, 280, 166, 179, 107, 172, 38
Offset: 1

Views

Author

Bhushan Bade, Sep 22 2016

Keywords

Examples

			a(18) = 1^2+2^2+3^2+6^2+9^2+1^2+8^2 = 196 because divisors of 18 are 1,2,3,6,9,18.
a(31) = 1^2+3^2+1^2 = 11 because divisors of 31 are 1,31.

Crossrefs

Cf. A003132.

Programs

  • Mathematica
    Table[Total@ Flatten@ Map[#^2 &, IntegerDigits@ Divisors@ n], {n, 61}] (* Michael De Vlieger, Sep 24 2016 *)
  • PARI
    ssd(n) = my(d=digits(n)); sum(k=1, #d, d[k]^2);
a(n) = sumdiv(n, d, ssd(d)); \\ Michel Marcus, Sep 22 2016

Extensions

More terms from Michel Marcus, Sep 22 2016

A276377 60th powers: a(n) = n^60.

Original entry on oeis.org

0, 1, 1152921504606846976, 42391158275216203514294433201, 1329227995784915872903807060280344576, 867361737988403547205962240695953369140625, 48873677980689257489322752273774603865660850176
Offset: 0

Views

Author

Bhushan Bade, Sep 01 2016

Keywords

Comments

Numbers which have square roots, cube roots, 4th, 5th and 6th roots.

Crossrefs

Cf. A122971 (n^30), A183085 (subsequence).

Programs

Formula

a(n) = n^60.
a(n) = A122971(n)^2. - Michel Marcus, Sep 02 2016

A276355 Sum of primes between 100*n and 100*n + 99.

Original entry on oeis.org

1060, 3167, 4048, 5612, 7649, 7760, 10316, 10466, 12719, 13330, 16826, 13780, 18775, 14759, 24773, 18666, 24679, 21022, 22230, 25413, 28750, 21398, 33781, 35381, 24452, 28057, 39905, 38474, 34168, 32407, 36560, 31544, 35669, 50157, 38009, 49688, 47439, 44994
Offset: 0

Views

Author

Bhushan Bade, Aug 31 2016

Keywords

Comments

The first occurrence of 0 in this sequence is as a(16718). - Robert Israel, Dec 28 2022

Examples

			Sum of primes in first interval of one hundred numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 is equal to first term i.e 1060.

Links

Crossrefs

Cf. A034387, A038822, A181098.

Programs

  • Maple
    R:= NULL: m:= 0: p:= 0: s:= 0:
while m <= 100 do
  p:= nextprime(p);
  r:= floor(p/100);
  if r = m then
    s:= s + p;
  else
    R:= R, s;
    if m < r-1 then R:= R, 0$(r-1-m) fi;
    s:= p;
    m:= r;
  fi
od:
R;
  • Mathematica
    Table[Total@ Select[Range[#, # + 99] &[100 n], PrimeQ], {n, 0, 37}] (* Michael De Vlieger, Sep 01 2016 *)

Formula

a(n) = A034387(100*(n+1)) - A034387(100*n). - Robert Israel, Aug 31 2016

Extensions

Definition by Omar E. Pol, Aug 31 2016

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

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