A277803 Minimum of A277802(n) and A004709(n).
1, 2, 3, 2, 5, 6, 7, 3, 10, 11, 12, 13, 14, 15, 17, 12, 19, 20, 21, 22, 23, 5, 26, 28, 29, 30, 31, 33, 34, 35, 6, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 7, 20, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 45, 76, 77, 78, 79
Offset: 1
Keywords
Links
- Peter Kagey, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Min /@ Transpose@ {#, Table[k = 1; While[! IntegerQ[(k #)^(1/3)], k++] &@ #[[n]]; k, {n, Length@ #}]} &@ Select[Range@ 80, FreeQ[FactorInteger@ #, {, k /; k > 2}] &] (* Michael De Vlieger, Nov 10 2016, after Jan Mangaldan at A004709 *) -
PARI
lista(n) = {n = ceil(1.21*n); my(l=List([1]), f); forprime(p=2,n, for(i=1,#l, if(l[i]*p<=n, listput(l, l[i] *p); if(l[i] * p^2<=n, listput(l, l[i]*p^2)))));listsort(l); for(i=2, #l, f=factor(l[i]); f[, 2] = vector(#f[,2], i, 3-(f[i, 2]%3))~; l[i] = min(l[i],factorback(f)));l} \\ David A. Corneth, Nov 01 2016 -
Python
from math import prod from sympy import mobius, factorint, integer_nthroot def A277803(n): def f(x): return n+x-sum(mobius(k)*(x//k**3) for k in range(1, integer_nthroot(x,3)[0]+1)) m, k = n, f(n) while m != k: m, k = k, f(k) return min(m,prod(p**(-e%3) for p, e in factorint(m).items())) # Chai Wah Wu, Aug 05 2024
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