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A280013
Numbers k such that sum of squarefree divisors of k > sum of squarefree divisors of m for all m < k.
5
1, 2, 3, 5, 6, 10, 14, 21, 22, 26, 30, 42, 66, 78, 102, 114, 130, 138, 170, 174, 186, 210, 318, 330, 390, 462, 510, 546, 570, 690, 798, 858, 870, 930, 1110, 1218, 1230, 1290, 1410, 1554, 1590, 1722, 1770, 1830, 1974, 2010, 2130, 2190, 2310, 2730, 3390, 3570, 3990, 4290, 4830, 5610
OFFSET
1,2
COMMENTS
Numbers k such that psi(rad(k)) > psi(rad(m)) for all m < k, where psi() is the Dedekind psi function (A001615) and rad() is the squarefree kernel (A007947).
Numbers k such that Sum_{d|k} mu(d)^2*d > Sum_{d|m} mu(d)^2*d for all m < k, where mu() is the Moebius function (A008683).
All terms are squarefree. - Robert Israel, Apr 19 2017
MAPLE
ssd:= n -> convert(select(numtheory:-issqrfree, numtheory:-divisors(n)), `+`):
M:= 0: A:= NULL:
for n from 1 to 10^5 do
r:= ssd(n);
if r > M then M:= r; A:= A, n fi
od:
A; # Robert Israel, Apr 19 2017
MATHEMATICA
mx = 0; t = {}; Do[u = DivisorSum[n, # &, SquareFreeQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 6000}]; t
PROG
(Python)
from sympy.ntheory.factor_ import core
from sympy import divisors
def s(n): return sum(list(filter(lambda i: core(i) == i, divisors(n))))
def ok(n):
m=1
while m<n:
if not s(n)>s(m): return False
m+=1
return True # Indranil Ghosh, Apr 16 2017
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 14 2017
STATUS
approved