A334903 Numbers k such that k and k+2 are both infinitary practical numbers (A334901).

6, 40, 54, 918, 1240, 1288, 1408, 1480, 1672, 1720, 1768, 1974, 2440, 2728, 2838, 2968, 3198, 3318, 4134, 4264, 4422, 4480, 4758, 5248, 6102, 6270, 6424, 7590, 7830, 10624, 11128, 13110, 13182, 14248, 15496, 15928, 16254, 16768, 18088, 19864, 21112, 21318, 21630

Offset

1,1

Links

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

Example

6 is a term since 6 and 6 + 2 = 8 are both infinitary practical numbers.

Mathematica

bin[n_] := 2^(-1 + Position[Reverse @ IntegerDigits[n, 2], _?(# == 1 &)] // Flatten); f[p_, e_] := p^bin[e]; icomp[n_] := Flatten[f @@@ FactorInteger[n]]; fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; infPracQ[n_] := Module[{f, p, e, prod = 1, ok = True}, If[n < 1 || (n > 1 && OddQ[n]), False, If[n == 1, True, r = Sort[icomp[n]]; Do[If[r[[i]] > 1 + isigma[prod], ok = False; Break[]]; prod = prod*r[[i]], {i, Length[r]}]; ok]]]; seq = {}; q1 = infPracQ[2]; Do[q2 = infPracQ[n]; If[q1 && q2, AppendTo[seq, n - 2]]; q1 = q2, {n, 4, 10^4, 2}]; seq

Crossrefs

Cf. A287681, A330871, A334882, A334900, A334901.

Sequence in context: A263955 A108937 A045565 * A200945 A217074 A110424

Adjacent sequences: A334900 A334901 A334902 * A334904 A334905 A334906

Keyword

nonn

Author

Amiram Eldar, May 16 2020

Status

approved