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 A358792 Numbers k such that for some r we have d(1) + ... + d(k - 1) = d(k + 1) + ... + d(k + r), where d(i) = A000005(i). 2
 3, 10, 16, 23, 24, 27, 42, 43, 45, 46, 49, 57, 60, 62, 67, 82, 92, 113, 117, 119, 122, 146, 151, 152, 157, 158, 159, 182, 188, 192, 193, 197, 198, 222, 223, 226, 228, 235, 242, 268, 270, 272, 274, 286, 288, 320, 323, 328, 334, 337, 361, 372, 373, 378, 381, 386 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These numbers might be called "divisor sequence balancing numbers", after the Behera and Panda link. Numbers k such that A006218(k-1) + A006218(k) is a term of A006218. - Robert Israel, Dec 01 2022 LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 A. Behera and G. K. Panda, On the square roots of triangular numbers, The Fibonacci Quarterly, 37.2 (1999), 98-105. EXAMPLE k = 3: d(1) + d(2) = d(4) = 3. Thus the balancing number k = 3 is a term. The balancer r is 1. k = 10: d(1) + ... + d(9) = d(11) + ... + d(16) = 23. Thus the balancing number k = 10 is a term. The balancer r is 6. d(i) = A000005(i). MAPLE Tau:= map(numtheory:-tau, [\$1..1000]): S:= ListTools:-PartialSums(Tau): A:=select(t -> member(S[t-1]+S[t], S), [\$2..1000]); # Robert Israel, Dec 01 2022 MATHEMATICA With[{m = 720}, d = DivisorSigma[0, Range[m]]; s = Accumulate[d]; Select[Range[2, m], MemberQ[s, 2*s[[#]] - d[[#]]] &]] (* Amiram Eldar, Dec 01 2022 *) PROG (Python) from sympy import divisor_count from itertools import count, islice def agen(): # generator of terms d, s, sset, i = [0, 1, 2], [0, 1, 3], set(), 3 for k in count(2): target = s[k-1] + s[k] while s[-1] < target: di = divisor_count(i); nexts = s[-1] + di; i += 1 d.append(di); s.append(nexts); sset.add(nexts) if target in sset: yield k print(list(islice(agen(), 56))) # Michael S. Branicky, Dec 04 2022 CROSSREFS Cf. A000005, A001109, A006218, A358797. Sequence in context: A242203 A093516 A246302 * A278041 A063209 A063109 Adjacent sequences: A358789 A358790 A358791 * A358793 A358794 A358795 KEYWORD nonn AUTHOR Ctibor O. Zizka, Dec 01 2022 EXTENSIONS More terms from Michael S. Branicky, Dec 01 2022 STATUS approved

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Last modified July 17 20:28 EDT 2024. Contains 374377 sequences. (Running on oeis4.)