

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.
Koninck & Luca show that this sequence is infinite.  Charles R Greathouse IV, Sep 08 2012


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
JeanMarie de Koninck and Florian Luca, Integers divisible by sums of powers of their prime factors, Journal of Number Theory, Volume 128, Issue 3, March 2008, Pages 557563.


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:


PROG

(PARI) is(n)=my(f=factor(n)[, 1]); #f>2&n%sum(i=1, #f, f[i]^2)==0 \\ Charles R Greathouse IV, May 23 2011
(PARI) is(n)=n>9 && !isprimepower(n) && n%norml2(factor(n)[, 1])==0 \\ Charles R Greathouse IV, Feb 03 2016


CROSSREFS

Cf. A066031.
Sequence in context: A061529 A115939 A168630 * A251278 A202897 A185518
Adjacent sequences: A190879 A190880 A190881 * A190883 A190884 A190885


KEYWORD

nonn


AUTHOR

Michel Lagneau, May 23 2011


STATUS

approved



