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

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

Author

Ilya Gutkovskiy, Apr 14 2017

Keywords

• nonn

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

Links

• Robert Israel, Table of n, a(n) for n = 1..500
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A001615, A002093, A002182, A007947, A008683, A034090, A048250, A174572.

Programs

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

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 ms(m): return False
        m+=1
    return True # Indranil Ghosh, Apr 16 2017