cp's OEIS Frontend

A280013 Numbers k such that sum of squarefree divisors of k > sum of squarefree divisors of m for all m < k.

%I A280013 #76 Jan 07 2024 01:49:01
%S A280013 1,2,3,5,6,10,14,21,22,26,30,42,66,78,102,114,130,138,170,174,186,210,
%T A280013 318,330,390,462,510,546,570,690,798,858,870,930,1110,1218,1230,1290,
%U A280013 1410,1554,1590,1722,1770,1830,1974,2010,2130,2190,2310,2730,3390,3570,3990,4290,4830,5610
%N A280013 Numbers k such that sum of squarefree divisors of k > sum of squarefree divisors of m for all m < k.
%C A280013 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).
%C A280013 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).
%C A280013 All terms are squarefree. - _Robert Israel_, Apr 19 2017
%H A280013 Robert Israel, <a href="/A280013/b280013.txt">Table of n, a(n) for n = 1..500</a>
%H A280013 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%p A280013 ssd:= n -> convert(select(numtheory:-issqrfree,numtheory:-divisors(n)),`+`):
%p A280013 M:= 0: A:= NULL:
%p A280013 for n from 1 to 10^5 do
%p A280013     r:= ssd(n);
%p A280013     if r > M then M:= r; A:= A, n fi
%p A280013 od:
%p A280013 A; # _Robert Israel_, Apr 19 2017
%t A280013 mx = 0; t = {}; Do[u = DivisorSum[n, # &, SquareFreeQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 6000}]; t
%o A280013 (Python)
%o A280013 from sympy.ntheory.factor_ import core
%o A280013 from sympy import divisors
%o A280013 def s(n): return sum(list(filter(lambda i: core(i) == i, divisors(n))))
%o A280013 def ok(n):
%o A280013     m=1
%o A280013     while m<n:
%o A280013         if not s(n)>s(m): return False
%o A280013         m+=1
%o A280013     return True # _Indranil Ghosh_, Apr 16 2017
%Y A280013 Cf. A001615, A002093, A002182, A007947, A008683, A034090, A048250, A174572.
%K A280013 nonn
%O A280013 1,2
%A A280013 _Ilya Gutkovskiy_, Apr 14 2017