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 A177791 Partial sums of A050705. 0

%I

%S 10,22,36,51,71,92,118,151,186,224,268,316,367,432,500,586,679,775,

%T 886,998,1114,1237,1398,1586,1787,1990,2196,2405,2615,2830,3051,3329,

%U 3626,3926,4230,4536,4857,5209,5565,5936,6320,6715,7113,7526,7946,8387,8858

%N Partial sums of A050705.

%C Partial sums of composite number such that when sum of its prime factors is added or subtracted becomes prime. The subsequence of primes in the partial sums begins: 71, 151, 367, 1237, 1787, 3329, 5209, 8387, 9343, 13781. The subsequence of partial sums which are themselves composite number such that when sum of their prime factors is added or subtracted becomes prime, begins: 10, 51, which other such fixed points are there?

%F a(n) = SUM[i=1..n] A050705(i) = SUM[i=1..n] {n such that n+A001414(n) is in A000040, and n-A001414(n) is in A000040}.

%e a(13) = 10 + 12 + 14 + 15 + 20 + 21 + 26 + 33 + 35 + 38 + 44 + 48 + 51 = 367 is prime.

%Y Cf. A000040, A001414, A050705, A050703-A050710.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, May 13 2010

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)