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.

A335398 Starts of runs of 4 consecutive numbers that have an equal number of unitary and nonunitary divisors (A048109).

Original entry on oeis.org

2068373, 2948373, 3571749, 3916374, 4730373, 4757750, 6755750, 8109125, 11290872, 12248872, 13071750, 13648311, 13903623, 15278247, 15448374, 15449749, 16793622, 17446374, 17991125, 19407624, 20080248, 20250375, 21594248, 22577750, 24190758, 25297622, 26140373
Offset: 1

Views

Author

Zak Seidov and Amiram Eldar, Jun 06 2020

Keywords

Examples

			2068373 is a term since 2068373, 2068374, 2068375 and 2068376 each have an equal number of unitary and nonunitary divisors. 2068373 and 2068375 each have 4 unitary divisors and 4 nonunitary divisors, 2068374 has 32 unitary divisors and 32 nonunitary divisors, and 2068376 has 8 unitary divisors and 8 nonunitary divisors.

Links

Crossrefs

Subsequence of A048109, A335328 and A335397.
Cf. A000005, A034444, A048105.

Programs

  • Mathematica
    q[n_] := DivisorSigma[0, n] == 2^(PrimeNu[n] + 1); v = q /@ Range[4]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 3]], {k, 5, 10^7}]; seq

A348099 Starts of runs of 3 consecutive numbers that have an equal number of unitary and nonunitary prime divisors (A348097).

Original entry on oeis.org

423, 603, 1250, 1375, 2007, 2523, 2527, 3175, 4075, 4203, 4374, 4923, 4948, 7442, 8991, 10375, 10467, 12591, 18027, 20402, 20575, 22023, 22687, 23823, 26071, 28375, 30231, 31507, 31850, 33271, 34623, 35574, 36162, 37348, 40023, 49975, 50274, 54475, 54511, 55323
Offset: 1

Views

Author

Amiram Eldar, Sep 30 2021

Keywords

Links

Crossrefs

Subsequence of A348097 and A348098.
Cf. A335397.

Programs

  • Mathematica
    q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), 1] == Length[e]/2; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 2]], {k, 4, 10^5}]; seq

Formula

423 is a term since 423 = 3^2 * 47, 423 + 1 = 424 = 2^3 * 53 and 423 + 2 = 425 = 5^2 * 17 all have one unitary prime divisor and one nonunitary prime divisor.

A335399 Starts of runs of 5 consecutive numbers that have an equal number of unitary and nonunitary divisors (A048109).

Original entry on oeis.org

146447622, 2259799749, 2559357269, 2647718871, 3660580374, 4262858871, 4708102374, 5188831623, 5341658373, 5494129749, 5728055749, 5876715750, 6127708374, 6455588247, 6608437623, 6612840374, 6617111750, 6689113623, 6722600373, 7456747623, 7923798375, 8272111445
Offset: 1

Views

Author

Zak Seidov and Amiram Eldar, Jun 06 2020

Keywords

Comments

Do longer runs of consecutive numbers with an equal number of unitary and nonunitary divisors exist for any length of run?
Starts of runs of 6 consecutive numbers that have an equal number of unitary and nonunitary divisors, from Giovanni Resta's bfile, 80566783622, 117243671750, 390773539750, 573122731621, 636972066374. - Zak Seidov, Jun 07 2020

Examples

			146447622 is a term since 146447622, 146447623, 146447624, 146447625 and 146447626 each have an equal number of unitary and nonunitary divisors. 146447622 has 32 unitary divisors and 32 nonunitary divisors, 146447623, 146447625 and 146447626 each have 8 and 8, and 146447624 has 16 and 16.

Links

Crossrefs

Subsequence of A048109, A335328, A335397 and A335398.
Cf. A000005, A034444, A048105.

Programs

  • Mathematica
    q[n_] := DivisorSigma[0, n] == 2^(PrimeNu[n] + 1); v = q /@ Range[5]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 4]], {k, 6, 3*10^8}]; seq
Showing 1-3 of 3 results.

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

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