A081061 Union of 3-smooth numbers and prime powers.
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 23, 24, 25, 27, 29, 31, 32, 36, 37, 41, 43, 47, 48, 49, 53, 54, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 96, 97, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 137, 139, 144, 149, 151, 157, 162, 163, 167
Offset: 1
Keywords
Links
- Jean-François Alcover, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
smooth3Q[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1; Select[Range[1000], PrimePowerQ[#] || smooth3Q[#]&] (* Jean-François Alcover, Oct 14 2021 *)
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Python
from sympy import integer_log, primepi, integer_nthroot def A081061(n): def f(x): return int(n+x-1+(a:=x.bit_length())+(b:=integer_log(x,3)[0])-sum((x//3**i).bit_length() for i in range(b+1))-sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, a))) m, k = n, f(n) while m != k: m, k = k, f(k) return m # Chai Wah Wu, Sep 16 2024
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