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A261614 Numbers that are neither prime (A000040) nor practical (A005153). 1
9, 10, 14, 15, 21, 22, 25, 26, 27, 33, 34, 35, 38, 39, 44, 45, 46, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 68, 69, 70, 74, 75, 76, 77, 81, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 110, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

a(5)=21 and it is neither prime nor practical. It is the 5th such occurrence.

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]]]; Select[Range[1, 1000], ! PracticalQ[#] && ! PrimeQ[#] &] (* using T. D. Noe's program A005153 *)

PROG

(PARI) isok(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) ;

for(n=1, 200, if(!isok(n) && !isprime(n), print1(n, ", "))) \\ Altug Alkan, Nov 19 2015

CROSSREFS

Cf. A000040, A005153, A225223.

Sequence in context: A110095 A169870 A061445 * A088710 A020199 A227943

Adjacent sequences:  A261611 A261612 A261613 * A261615 A261616 A261617

KEYWORD

nonn

AUTHOR

Frank M Jackson, Nov 18 2015

STATUS

approved

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Last modified July 26 16:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)