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

0,2

Comments

a(n) is analogous to A033844.

Links

Table of n, a(n) for n=0..32.

Formula

a(n) = A005153(A000079(n)). - Michel Marcus, Nov 12 2015

Example

a(7) = A005153(128) = 594.

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 *)

Prog

(Python)
from math import prod
from itertools import count
from sympy import factorint
def A225316(n):
    if n:
        c, k = 1, 1<<n
        for m in count(2, 2):
            f = list(factorint(m).items())
            if all(f[i][0] <= 1+prod((f[j][0]**(f[j][1]+1)-1)//(f[j][0]-1) for j in range(i)) for i in range(len(f))):
                c += 1
                if c == k:
                    return m
    else:
        return 1 # Chai Wah Wu, Aug 04 2023

Crossrefs

Cf. A000079, A005153, A033844, A225559, A322371.

Sequence in context: A291519 A027556 A195584 * A272934 A192708 A233531

Adjacent sequences: A225313 A225314 A225315 * A225317 A225318 A225319

Keyword

nonn

Author

Frank M Jackson, May 05 2013

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

Status

approved