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A280013
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Numbers n such that sum of squarefree divisors of n > sum of squarefree divisors of m for all m < n.
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5
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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
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OFFSET
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1,2
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COMMENTS
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Numbers n such that psi(rad(n)) > psi(rad(m)) for all m < n, where psi() is the Dedekind psi function (A001615) and rad() is the squarefree kernel (A007947).
Numbers n such that Sum_{d|n} mu(d)^2*d > Sum_{d|m} mu(d)^2*d for all m < n, where mu() is the Moebius function (A008683).
All terms are squarefree. - Robert Israel, Apr 19 2017
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..500
Index entries for sequences related to sums of divisors
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MAPLE
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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
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MATHEMATICA
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mx = 0; t = {}; Do[u = DivisorSum[n, # &, SquareFreeQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 6000}]; t
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PROG
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(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
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CROSSREFS
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Cf. A001615, A002093, A002182, A007947, A008683, A034090, A048250, A174572.
Sequence in context: A325714 A325715 A325534 * A039840 A039845 A347868
Adjacent sequences: A280010 A280011 A280012 * A280014 A280015 A280016
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Apr 14 2017
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STATUS
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approved
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