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A321308 Practical numbers k such that k^4 + 2 is also practical. 1
2, 16, 28, 160, 280, 512, 520, 644, 820, 1040, 1204, 1640, 2000, 2072, 2288, 2720, 2920, 3416, 3800, 3976, 4648, 4664, 4736, 5312, 5600, 6136, 6188, 6496, 6968, 7936, 8080, 8300, 8944, 11792, 11984, 12512, 12656, 13624, 14060, 14416, 14768, 15680, 16000, 16384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are infinitely many practical numbers k such that k^4 + 2 is also practical (see Wang and Sun Theorem 1.3). - Michel Marcus, Nov 03 2018

LINKS

Table of n, a(n) for n=1..44.

Li-Yuan Wang and Zhi-Wei Sun, On practical numbers of some special forms, arXiv preprint arXiv:1809.01532 [math.NT], 2018. See Theorem 1.3 p. 3.

EXAMPLE

2 and 18 = 2^4 + 2 are practical, hence 2 is a term. - Michel Marcus, Nov 03 2018

MATHEMATICA

PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1 || (n>1 && OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e} = Transpose[f]; Do[If[p[[i]] > 1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; (* A005153 *)

a[q_]:=If[PracticalQ[q] && PracticalQ[q^4+2], q]; DeleteCases[Array[a, 25000], Null]

PROG

(PARI) ispractical(n) = bittest(n, 0) && return(n==1); my(P=1); n && !for(i=2, #n=factor(n)~, n[1, i]>1+(P*=sigma(n[1, i-1]^n[2, i-1])) && return); \\ A005153

isok(n) = ispractical(n) && ispractical(n^4+2); \\ Michel Marcus, Nov 03 2018

CROSSREFS

Cf. A005153 (practical numbers), A000583.

Sequence in context: A113933 A127871 A242933 * A109210 A056707 A069256

Adjacent sequences:  A321305 A321306 A321307 * A321309 A321310 A321311

KEYWORD

nonn

AUTHOR

Stefano Spezia, Nov 03 2018

STATUS

approved

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Last modified September 18 15:48 EDT 2020. Contains 337169 sequences. (Running on oeis4.)