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A195349
Numbers n such that Sum_{k=1..n} d(k) divides Product_{k=1..n} d(k), where d(k) is the number of divisors of k.
1
1, 7, 19, 41, 57, 64, 68, 133, 145, 149, 164, 235, 267, 291, 317, 336, 358, 419, 433, 503, 528, 566, 599, 612, 659, 726, 801, 927, 1017, 1035, 1077, 1118, 1190, 1206, 1213, 1281, 1297, 1309, 1320, 1323, 1367, 1446, 1473, 1485, 1516, 1595, 1611, 1634, 1941
OFFSET
1,2
COMMENTS
d(k) is sometimes called tau(k) or sigma_0(k). Is this sequence infinite?
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..2000 (term 1..500 from Harvey P. Dale)
MATHEMATICA
t = {}; a = 0; b = 1; Do[a = a + DivisorSigma[0, n]; b = b*DivisorSigma[0, n]; If[Mod[b, a] == 0, AppendTo[t, n]], {n, 2000}]; t (* T. D. Noe, Sep 16 2011 *)
With[{c=DivisorSigma[0, Range[2000]]}, Position[Thread[{FoldList[ Times, c], Accumulate[ c]}], _?(Divisible[#[[1]], #[[2]]]&), 1, Heads->False]] // Flatten (* Harvey P. Dale, Apr 14 2019 *)
PROG
(Python)
from sympy import divisor_count
A195349_list, s, p = [], 0, 1
for k in range(1, 10**4):
d = divisor_count(k)
s += d
p *= d
if p % s == 0:
A195349_list.append(k) # Chai Wah Wu, Oct 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Carl Najafi, Sep 16 2011
STATUS
approved