A080785 Least p-smooth number not less than n, where p is the smallest prime factor of n.

1, 2, 3, 4, 5, 8, 7, 8, 9, 16, 11, 16, 13, 16, 16, 16, 17, 32, 19, 32, 24, 32, 23, 32, 25, 32, 27, 32, 29, 32, 31, 32, 36, 64, 36, 64, 37, 64, 48, 64, 41, 64, 43, 64, 48, 64, 47, 64, 49, 64, 54, 64, 53, 64, 60, 64, 64, 64, 59, 64, 61, 64, 64, 64, 72, 128, 67, 128, 72, 128, 71

Offset

1,2

Comments

a(n)<=2^k for n<=2^k.

a(n)=n for n in A000961. - Ivan Neretin, Apr 30 2016

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Smooth Number.

Mathematica

a[n_] := Module[{p, k}, p = FactorInteger[n][[1, 1]]; For[k = n, True, k++, If[FactorInteger[k][[-1, 1]] <= p, Return[k]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 15 2021 *)

Prog

(Python)
from sympy import integer_log, prevprime, primefactors
from oeis_sequences.OEISsequences import bisection
def A080785(n):
    if n == 1: return 1
    def g(x, m): return x.bit_length() if m==2 else sum(g(x//(m**i), prevprime(m))for i in range(integer_log(x, m)[0]+1))
    k = g(n-1, p:=min(primefactors(n)))+1
    def f(x): return k+x-g(x, p)
    return bisection(f, k, k) # Chai Wah Wu, Mar 13 2026

Crossrefs

Cf. A020639, A006530.

Cf. A000079, A003586, A051037, A002473, A051038, A080197, A080681, A080682, A080683.

Sequence in context: A258831 A098098 A326066 * A319605 A352047 A245822

Adjacent sequences: A080782 A080783 A080784 * A080786 A080787 A080788

Keyword

nonn

Author

Reinhard Zumkeller, Mar 12 2003

Status

approved