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

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

1,2

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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[#] &]

Crossrefs

Intersection of A361922 and A361924.

Cf. A091732.

Similar sequences: A359417, A359418.

Sequence in context: A005392 A001196 A330941 * A096854 A013191 A332959

Adjacent sequences: A361922 A361923 A361924 * A361926 A361927 A361928

Keyword

nonn

Author

Amiram Eldar, Mar 30 2023

Status

approved