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A179435 For positive n with prime decomposition n = Product_{j=1..m} (p_j^k_j) define a_n = Sum_{j=1..m} (p_j*k_j) and b_n = Sum_{j=1..m} (p_j^k_j). This sequence gives those n for which a_n and b_n are both prime and unequal. 1

%I

%S 40,48,54,88,108,184,250,384,424,432,448,808,864,1048,1216,1384,1528,

%T 1575,1680,1792,1864,1890,2104,2184,2457,2925,2944,3080,3120,3328,

%U 3510,3696,3712,3915,4125,4158,4288,4504,4744,4950,5224,5488,5632,5928,5940,6240

%N For positive n with prime decomposition n = Product_{j=1..m} (p_j^k_j) define a_n = Sum_{j=1..m} (p_j*k_j) and b_n = Sum_{j=1..m} (p_j^k_j). This sequence gives those n for which a_n and b_n are both prime and unequal.

%C Is the sequence infinite?

%C Odd terms in the sequence are: a(18) = 1575, a(25) = 2457, a(26) = 2925, a(34) = 3915, a(35) = 4125, a(47) = 6345, a(50) = 6669, ...

%H Alois P. Heinz, <a href="/A179435/b179435.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 40 = 2^3*5^1, with a = 11 and b = 13.

%e a(2) = 48 = 2^4*3^1, with a = 11 and b = 19.

%e Notice that a and b are both prime and not equal.

%p a:= proc(n) option remember; local an, bn, k, l;

%p for k from 1 +`if` (n=1, 0, a(n-1)) do

%p l:= ifactors(k)[2];

%p an:= add( i[1] * i[2], i=l);

%p bn:= add( i[1] ^ i[2], i=l);

%p if isprime(an) and isprime(bn) and an<>bn then break fi

%p od; k

%p end:

%p seq(a(n), n=1..50); # _Alois P. Heinz_, Jan 20 2011

%K nonn

%O 1,1

%A _Bobby Browning_ and Rohan Hemasinha (rhemasin(AT)uwf.edu), Jan 07 2011

%E More terms from _Alois P. Heinz_, Jan 20 2011

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Last modified May 19 12:49 EDT 2019. Contains 323393 sequences. (Running on oeis4.)