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A280013 Numbers n such that sum of squarefree divisors of n > sum of squarefree divisors of m for all m < n. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..500

Index entries for sequences related to sums of divisors

MAPLE

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 14 2017

STATUS

approved

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Last modified May 20 07:42 EDT 2022. Contains 353852 sequences. (Running on oeis4.)