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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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, ... LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 EXAMPLE 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. MAPLE 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);         an:= add( i * i, i=l);         bn:= add( i ^ i, 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 CROSSREFS Sequence in context: A204746 A197734 A114839 * A120382 A290017 A062909 Adjacent sequences:  A179432 A179433 A179434 * A179436 A179437 A179438 KEYWORD nonn AUTHOR Bobby Browning and Rohan Hemasinha (rhemasin(AT)uwf.edu), Jan 07 2011 EXTENSIONS More terms from Alois P. Heinz, Jan 20 2011 STATUS approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)