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 A180746 Partial sums of A004144. 0
 1, 3, 6, 10, 16, 23, 31, 40, 51, 63, 77, 93, 111, 130, 151, 173, 196, 220, 247, 275, 338, 338, 371, 407, 445, 487, 530, 574, 620, 667, 715, 764, 818, 874, 931, 990, 1052, 1115, 1179, 1245, 1312, 1381, 1452, 1524, 1600, 1677, 1756, 1837, 1920, 2090, 2090, 2178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Partial sums of nonhypotenuse numbers (squares are not sums of 2 distinct nonzero squares). Partial sums of numbers with no prime factors of form 4*k+1. Partial sums of complement of A009003. Primes in the partial sums begin: 3, 23, 31, x, 151, 173, 487, 1381, 3533. Squares in the partial sum begin 1, 196, 1600. LINKS FORMULA a(n) = sum[i=1..n] A004144(i). EXAMPLE a(7) = 1 + 2 + 3 + 4 + 6 + 7 + 8 = 31 is prime. MATHEMATICA fQ[n_] := If[n > 1, First@ Union@ Mod[ First@# & /@ FactorInteger@ n, 4] != 1, True]; Accumulate@ Select[ Range@ 90, fQ] CROSSREFS Cf. A004144, A009003. Sequence in context: A194144 A025701 A025744 * A025714 A025729 A011913 Adjacent sequences:  A180743 A180744 A180745 * A180747 A180748 A180749 KEYWORD nonn AUTHOR Jonathan Vos Post, Sep 19 2010 STATUS approved

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