A225316 a(n) = practical(2^n) where practical(n) is the n-th practical number (A005153).
1, 2, 6, 18, 42, 108, 270, 594, 1350, 3008, 6678, 14620, 31724, 67712, 143792, 305856, 651126, 1377918, 2908308, 6120672, 12848472, 26854938, 55963260, 116389896, 241526012, 500796416, 1037764968, 2147851712, 4440630150, 9176799780, 18946755918, 39092425578, 80569691202
Offset: 0
Keywords
Examples
a(7) = A005153(128) = 594.
Programs
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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]]]; nextpractical[n1_]:=(m1=n1+1; While[!PracticalQ[m1],m1++]; m1); Table[Nest[nextpractical,0,2^n],{n,0,20}] (* using T. D. Noe's program A005153 *) -
Python
from math import prod from itertools import count from sympy import factorint def A225316(n): if n: c, k = 1, 1<
Chai Wah Wu, Aug 04 2023
Formula
Extensions
a(26)-a(27) from Chai Wah Wu, Aug 07 2023
a(28)-a(29) from David A. Corneth, Aug 07 2023
More terms from David A. Corneth, Aug 14 2023
Comments