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

1,2

Comments

With the exception of the first term, each term appears exactly two times.

For how many n < m is A004709(n) < A277802(n)? It seems about m for large m. - David A. Corneth, Nov 01 2016

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

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 *)

Prog

\\ List of the first about n terms (probably a bit more).
(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

Crossrefs

Cf. A004709, A277802.

Sequence in context: A080979 A287620 A304491 * A062789 A375240 A066069

Adjacent sequences: A277800 A277801 A277802 * A277804 A277805 A277806

Keyword

nonn

Author

Peter Kagey, Oct 31 2016

Status

approved