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 A362986 a(n) = A000203(A036966(n)), the sum of divisors of the n-th cubefull number A036966(n). 6
 1, 15, 31, 40, 63, 127, 121, 156, 255, 600, 364, 511, 400, 1240, 1023, 781, 1815, 1093, 2520, 2340, 2047, 3751, 1464, 5080, 5460, 4836, 4095, 3280, 2380, 2801, 7623, 6000, 3906, 6240, 10200, 11284, 9828, 8191, 5220, 11715, 15367, 12400, 16395, 9841, 7240, 20440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Rafael Jakimczuk and Matilde Lalín, Asymptotics of sums of divisor functions over sequences with restricted factorization structure, Notes on Number Theory and Discrete Mathematics, Vol. 28, No. 4 (2022), pp. 617-634, eq. (7). FORMULA Sum_{a(k) < x} a(k) = c * x^(4/3) + O(x^(113/96 + eps)), where c = A362985 * A362974 / 4 = 2.8912833599... (Jakimczuk and Lalín, 2022). Sum_{k=1..n} a(k) ~ c * n^4, where c = A362985 / (4 * A362974^3) = 0.006135085083... . MATHEMATICA DivisorSigma[1, Select[Range[10^4], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 2 &]] PROG (PARI) lista(kmax) = for(k = 1, kmax, if(k==1 || vecmin(factor(k)[, 2]) > 2, print1(sigma(k), ", "))); (Python) from itertools import count, islice from math import prod from sympy import factorint def A362986_gen(): # generator of terms for n in count(1): f = factorint(n) if all(e>2 for e in f.values()): yield prod((p**(e+1)-1)//(p-1) for p, e in f.items()) A362986_list = list(islice(A362986_gen(), 20)) # Chai Wah Wu, May 21 2023 CROSSREFS Cf. A000203, A036966, A180114, A362974, A362985. Sequence in context: A249764 A202522 A054305 * A041442 A041440 A042017 Adjacent sequences: A362983 A362984 A362985 * A362987 A362988 A362989 KEYWORD nonn AUTHOR Amiram Eldar, May 12 2023 STATUS approved

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Last modified September 15 02:41 EDT 2024. Contains 375930 sequences. (Running on oeis4.)