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 A358797 Numbers r such that for some k we have d(1) + ... + d(k - 1) = d(k + 1) + ... + d(k + r), where d(i) = A000005(i). 2
 1, 6, 11, 16, 17, 19, 31, 32, 34, 34, 37, 43, 45, 47, 52, 63, 72, 89, 92, 92, 97, 117, 120, 120, 126, 126, 126, 146, 150, 154, 156, 158, 159, 178, 179, 182, 184, 190, 197, 217, 219, 221, 222, 232, 234, 260, 264, 267, 272, 276, 298, 304, 306, 310, 314, 317, 317 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These numbers might be called "divisor sequence balancers" after Behera and Panda. 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 r = 1: d(1) + d(2) = d(4) = 3. Thus the balancer r = 1 is a term. The balancing number k = 3. r = 6: d(1) + ... + d(9) = d(11) + ... + d(16) = 23. Thus the balancer r = 6 is a term. The balancing number k = 10. d(i) = A000005(i). MATHEMATICA With[{m = 720}, d = DivisorSigma[0, Range[m]]; s = Accumulate[d]; e = 2*s - d; i = Select[Range[2, m], MemberQ[s, e[[#]]] &]; Position[s, #][[1, 1]] & /@ e[[i]] - i] (* Amiram Eldar, Dec 01 2022 *) PROG (Python) from sympy import divisor_count from itertools import count, islice def agen(): # generator of terms d, s, sdict, i = [0, 1, 2], [0, 1, 3], dict(), 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); sdict[nexts] = i-1 if target in sdict: yield sdict[target] - k print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 04 2022 CROSSREFS Cf. A000005, A001109, A006218, A358792. Sequence in context: A141352 A276973 A248351 * A190552 A305408 A315437 Adjacent sequences: A358794 A358795 A358796 * A358798 A358799 A358800 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 February 26 06:43 EST 2024. Contains 370335 sequences. (Running on oeis4.)