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 1-3 of 3 results.

A333928 Recursive abundant numbers: numbers k such that A333926(k) > 2*k.

Original entry on oeis.org

12, 18, 20, 30, 36, 42, 60, 66, 70, 78, 84, 90, 100, 102, 108, 114, 120, 126, 132, 138, 140, 144, 150, 156, 168, 174, 180, 186, 196, 198, 204, 210, 220, 222, 228, 234, 240, 246, 252, 258, 260, 270, 276, 282, 294, 300, 306, 308, 318, 324, 330, 336, 340, 342, 348
Offset: 1

Views

Author

Amiram Eldar, Apr 10 2020

Keywords

Examples

			12 is a term since A333926(12) = 28 > 2 * 12.

Links

Crossrefs

Cf. A333926, A333927.
Analogous sequences: A005101, A034683 (unitary), A064597 (nonunitary), A129575 (exponential), A129656 (infinitary), A292982 (bi-unitary).

Programs

  • Mathematica
    recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recDivSum[1] = 1; recDivSum[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[350], recDivSum[#] > 2*# &]

A333929 Lesser of recursive amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) = A333926(k) - k is the sum of proper recursive divisors of k.

Original entry on oeis.org

220, 366, 2620, 3864, 5020, 16104, 16536, 26448, 29760, 43524, 63020, 67344, 69615, 100485, 122265, 142290, 142310, 196248, 196724, 198990, 239856, 240312, 280540, 308620, 309264, 319550, 326424, 341904, 348840, 366792, 469028, 522405, 537744, 580320, 647190, 661776
Offset: 1

Views

Author

Amiram Eldar, Apr 10 2020

Keywords

Comments

The larger counterparts are in A333930.

Examples

			220 is a terms since A333926(220) - 220 = 284 and A333926(284) - 284 = 220.

Links

Crossrefs

Cf. A333926, A333927, A333930.
Analogous sequences: A002025, A002952 (unitary), A126165 (exponential), A126169 (infinitary), A292980 (bi-unitary).

Programs

  • Mathematica
    recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recDivSum[1] = 1; recDivSum[n_] := Times @@ (f @@@ FactorInteger[n]); s[n_] := recDivSum[n] - n; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, n]], {n, 1, 10^5}]; seq

A333930 Larger of recursive amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) = A333926(k) - k is the sum of proper recursive divisors of k.

Original entry on oeis.org

284, 378, 2924, 4584, 5564, 16632, 16728, 28752, 30912, 53692, 76084, 69552, 87633, 124155, 139815, 179118, 168730, 225096, 202444, 256338, 245904, 266568, 365084, 389924, 320016, 430402, 391656, 353616, 387720, 393528, 486178, 525915, 555216, 642720, 814698, 682896
Offset: 1

Views

Author

Amiram Eldar, Apr 10 2020

Keywords

Comments

The terms are ordered according to their lesser counterparts (A333929).

Examples

			284 is a terms since A333926(284) - 284 = 220 and A333926(220) - 220 = 284.

Links

Crossrefs

Cf. A333926, A333927, A333929.
Analogous sequences: A002046, A002953 (unitary), A126166 (exponential), A126170 (infinitary), A292981 (bi-unitary).

Programs

  • Mathematica
    recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recDivSum[1] = 1; recDivSum[n_] := Times @@ (f @@@ FactorInteger[n]); s[n_] := recDivSum[n] - n; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 10^5}]; seq
Showing 1-3 of 3 results.

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