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A179435
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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.
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1
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40, 48, 54, 88, 108, 184, 250, 384, 424, 432, 448, 808, 864, 1048, 1216, 1384, 1528, 1575, 1680, 1792, 1864, 1890, 2104, 2184, 2457, 2925, 2944, 3080, 3120, 3328, 3510, 3696, 3712, 3915, 4125, 4158, 4288, 4504, 4744, 4950, 5224, 5488, 5632, 5928, 5940, 6240
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OFFSET
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1,1
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COMMENTS
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Is the sequence infinite?
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, ...
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..1000
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EXAMPLE
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a(1) = 40 = 2^3*5^1, with a = 11 and b = 13.
a(2) = 48 = 2^4*3^1, with a = 11 and b = 19.
Notice that a and b are both prime and not equal.
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MAPLE
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a:= proc (n) option remember; local an, bn, k, l;
for k from 1 +`if` (n=1, 0, a(n-1)) do
l:= ifactors(k)[2];
an:= add( i[1] * i[2], i=l);
bn:= add( i[1] ^ i[2], i=l);
if isprime(an) and isprime(bn) and an<>bn then break fi
od; k
end:
seq (a(n), n=1..50); # Alois P. Heinz, Jan 20 2011
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CROSSREFS
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Sequence in context: A204746 A197734 A114839 * A120382 A062909 A167327
Adjacent sequences: A179432 A179433 A179434 * A179436 A179437 A179438
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KEYWORD
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nonn
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AUTHOR
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Bobby Browning and Rohan Hemasinha (rhemasin(AT)uwf.edu), Jan 07 2011
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EXTENSIONS
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More terms from Alois P. Heinz, Jan 20 2011
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STATUS
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approved
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