OFFSET
1,6
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Bernd C. Kellner, On a product of certain primes, J. Number Theory, 179 (2017), 126-141; arXiv:1705.04303 [math.NT], 2017.
Bernd C. Kellner and Jonathan Sondow, Power-Sum Denominators, Amer. Math. Monthly, 124 (2017), 695-709; arXiv:1705.03857 [math.NT], 2017.
Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, Integers 21 (2021), #A52, 21 pp.; arXiv:1902.10672 [math.NT], 2019.
FORMULA
EXAMPLE
6 = 2 * 3, and 6 = 110_2 in base 2 with 1+1+0 >= 2, but 6 = 20_3 in base 3 with 2+0 = 2 < 3, so a(6) = 2.
MAPLE
g:= proc(n, p) convert(convert(n, base, p), `+`) >= p end proc:
f:= proc(n) local p;
convert(select(p -> g(n, p), numtheory:-factorset(n)), `*`)
end proc:
map(f, [$1..100]); # Robert Israel, Feb 28 2019
MATHEMATICA
SD[n_, p_] := If[n < 2, 0, Plus @@ IntegerDigits[n, p]];
LP[n_] := Transpose[FactorInteger[n]][[1]];
DD1[n_] := Times @@ Select[LP[n], SD[n, #] >= # &];
Table[DD1[n], {n, 1, 100}]
PROG
(Python)
from math import prod
from sympy.ntheory import digits
from sympy import primefactors as pf
def a(n): return prod(p for p in pf(n) if sum(digits(n, p)[1:]) >= p)
print([a(n) for n in range(1, 98)]) # Michael S. Branicky, Jul 03 2022
CROSSREFS
KEYWORD
AUTHOR
Bernd C. Kellner and Jonathan Sondow, Feb 24 2019
STATUS
approved