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.

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A361925 Infinitary phi-practical (A361922) whose infinitary divisors have distinct values of the infinitary totient function iphi (A091732).

Original entry on oeis.org

1, 3, 12, 15, 60, 105, 108, 132, 156, 165, 195, 240, 255, 660, 960, 1020, 1140, 1155, 1188, 1380, 1680, 1716, 1728, 1740, 1785, 1860, 1995, 2052, 2145, 2220, 2244, 2415, 2460, 2484, 2496, 2508, 2580, 2640, 2652, 2805, 2820, 2940, 3036, 3045, 3120, 3132, 3135, 3180
Offset: 1

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Author

Amiram Eldar, Mar 30 2023

Keywords

Comments

An infinitary phi-practical number k is a number k such that each number in the range 1..k is a subsum of the multiset {iphi(d) | d infinitary divisor of k}. This sequence is restricted to cases in which all the values in this multiset are distinct.

Crossrefs

Intersection of A361922 and A361924.
Cf. A091732.
Similar sequences: A359417, A359418.

Programs

  • Mathematica
    f[p_, e_] := p^(2^(-1 + Position[Reverse@ IntegerDigits[e, 2], 1]));
    iphi[1] = 1; iphi[n_] := Times @@ (Flatten@ (f @@@ FactorInteger[n]) - 1);
    idivs[n_] := Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]; idivs[1] = {1};
    iPhiPracticalQ[n_] := Module[{s = Sort@Map[iphi, idivs[n]], ans = True}, Do[If[s[[j]] > Sum[s[[i]], {i, 1, j - 1}] + 1, ans = False; Break[]], {j, 1, Length[s]}]; ans];
    Select[Range[3200], UnsameQ @@ iphi /@ idivs[#] && iPhiPracticalQ[#] &]
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