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 A108174 Partial sums of the positive integers n according to the rule: if n is square then subtract n, otherwise add n. 1
 0, -1, 1, 4, 0, 5, 11, 18, 26, 17, 27, 38, 50, 63, 77, 92, 76, 93, 111, 130, 150, 171, 193, 216, 240, 215, 241, 268, 296, 325, 355, 386, 418, 451, 485, 520, 484, 521, 559, 598, 638, 679, 721, 764, 808, 853, 899, 946, 994, 945, 995, 1046, 1098, 1151, 1205, 1260, 1316, 1373, 1431, 1490, 1550, 1611, 1673, 1736, 1672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{i=1..n} i*(-1)^tau(i), where tau(i) = A000005(i). - Ridouane Oudra, Oct 08 2019 MATHEMATICA Accumulate[Table[If[IntegerQ[Sqrt[n]], -n, n], {n, 0, 70}]] (* Harvey P. Dale, Jan 17 2017 *) PROG (PARI) g(n) = my(s=0); for(x=0, n, if(issquare(x), s-=x, s+=x); print1(s, ", ")) (MAGMA) [0] cat [&+[i*(-1)^#Divisors(i):i in [1..n]]:n in [1..70]]; // Marius A. Burtea, Oct 09 2019 CROSSREFS Cf. A000005, A000290 (squares). Sequence in context: A164108 A064520 A267313 * A134530 A308678 A184365 Adjacent sequences:  A108171 A108172 A108173 * A108175 A108176 A108177 KEYWORD easy,sign AUTHOR Cino Hilliard, Jun 13 2005 STATUS approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)