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A334882
Numbers k such that k and k+2 are both primitive practical numbers (A267124).
5
28, 304, 306, 340, 460, 462, 858, 868, 1482, 1768, 1974, 2440, 2728, 2838, 2860, 3318, 3738, 4134, 4264, 4288, 4420, 4422, 5236, 5694, 6100, 6102, 7590, 8814, 9040, 9042, 10218, 11128, 11620, 11778, 12558, 12978, 13110, 14320, 14382, 14670, 15568, 16048, 16110
OFFSET
1,1
LINKS
EXAMPLE
28 is a term since 28 and 28 + 2 = 30 are both primitive practical numbers.
MATHEMATICA
f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[fct_] := (ind = Position[fct[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), _?(# > 1 &)]) == {}; pracTestQ[fct_, k_] := Module[{f = fct}, f[[k, 2]] -= 1; pracQ[f]]; primPracQ[n_] := Module[{fct = FactorInteger[n]}, pracQ[fct] && AllTrue[Range@Length[fct], fct[[#, 2]] == 1 || ! pracTestQ[fct, #] &]]; Select[Range[2, 16200, 2], primPracQ[#] && primPracQ[# + 2] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 14 2020
STATUS
approved