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Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) is not 0 (mod n), but 2 * (1^d + 2^d + 3^d + ... + d^d) is 0 (mod d) for each other d | n.
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%I #9 Jan 10 2017 08:11:26

%S 6,20,110,272,506,812,2162,2756,3422,4970,6806,7832,11342,12656,17030,

%T 18632,22052,27722,29756,31862,36290,38612,51302,54056,56882,62750,

%U 65792,68906,72092,85556,96410,100172,120062,124256,128522

%N Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) is not 0 (mod n), but 2 * (1^d + 2^d + 3^d + ... + d^d) is 0 (mod d) for each other d | n.

%H Charles R Greathouse IV, <a href="/A280187/b280187.txt">Table of n, a(n) for n = 1..4000</a>

%o (PARI) has(n)=my(f=factor(n)[,1]); for(i=1,#f, if(n%(f[i]-1)==0 && f[i]>2, return(1))); 0

%o is(n)=if(n%2, return(0)); if(n%3==0, return(n==6)); if(n%20==0, return(n==20)); if(!has(n), return(0)); my(f=factor(n)[,1]); for(i=1,#f, if(has(n/f[i]), return(0))); 1 \\ _Charles R Greathouse IV_, Dec 28 2016

%Y Primitive elements of A228870.

%Y Subsequence of A002943. Also a subsequence of A028689, A036689, A053198, A068377, A079143, A128672, A220211 and other sequences ...- _Paolo P. Lava_, Jan 10 2017

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Dec 28 2016