

A190882


Numbers other than prime powers divisible by the sum of the squares of their prime divisors.


4



46206, 72105, 73346, 92412, 96096, 97440, 98098, 99528, 113883, 117040, 127680, 134805, 138618, 143520, 146692, 150024, 165880, 165886, 184824, 192192, 194880, 196196, 199056, 216315, 234080, 255360, 269192, 276640, 277236, 287040, 288288, 292320, 293384, 294216, 298584, 300048, 331760
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OFFSET

1,1


COMMENTS

The number of distinct prime divisors of n is > = 3, because if n = p^a * q^b where p and q are distinct primes, p^2+q^2  n => p+q ==0 (mod p) or 0 (mod (q), but p==0 (mod q), or q==0 (mod p) is impossible.


LINKS



EXAMPLE

46206 is in the sequence because the prime distinct divisors of this number are {2, 3, 17, 151} and 2^2 + 3^2 + 17^2 + 151^2 = 23103, then 46206 = 23103*2.


MAPLE

with(numtheory):for n from 1 to 200000 do:x:=factorset(n):n1:=nops(x):s:=0:for
p from 1 to n1 do: s:=s+x[p]^2:od:if n1 >= 2 and irem(n, s)=0 then printf(`%d, `, n):else fi:od:


MATHEMATICA

Select[Range[2, 332000], !PrimePowerQ[#]&&Divisible[#, Total[Select[ Divisors[#], PrimeQ]^2]]&] (* Harvey P. Dale, May 24 2022 *)


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



