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 A344015 2-adic valuation of A344014(n). 4
 3, 12, 20, 28, 35, 46, 52, 60, 67, 76, 86, 94, 101, 111, 116, 124, 131, 140, 148, 156, 163, 176, 182, 190, 197, 206, 215, 223, 230, 244, 244, 252, 259, 268, 276, 284, 291, 302, 308, 316, 323, 332, 344, 352, 359, 369, 374, 382, 389, 398, 406, 414, 421, 433, 439, 447, 454, 463, 472, 480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These numbers are integers, even if it should turn out that some of the terms of A344014 are fractional. Jan Vonk observed that a(n) ~ 8*n. - Robin Visser, Jul 29 2023 LINKS Robin Visser, Table of n, a(n) for n = 1..200 Jan Vonk, Overconvergent modular forms and their explicit arithmetic, Bulletin of the American Mathematical Society 58.3 (2021): 313-356. FORMULA a(n) = A007814(A344014(n)). - Michel Marcus, Jul 30 2023 EXAMPLE From Robin Visser, Jul 29 2023: (Start) An expansion for U_2 j^_1 in terms of powers of j^-1 is given by U_2 j^-1 = -744*j^-1 - 140914688*j^-2 - 16324041375744*j^-3 - .... The first coefficient factors as -744 = -2^3 * 3 * 31, so a(1) = 3. The second coefficient factors as -140914688 = -2^12 * 34403, so a(2) = 12. The third coefficient factors as -16324041375744 = -2^20 * 3 * 79 * 65687, so a(3) = 20. (End) PROG (Sage) def a(n): j1 = sum([1]+[240*sigma(k, 3)*x^k for k in range(1, 2*n)]) j2 = product([x]+[(1-x^k)^24 for k in range(1, 2*n)]) jinv = (j2/j1^3).taylor(x, 0, 2*n) U2jinv = sum([jinv.coefficient(x^(2*k))*x^k for k in range(0, 2*n)]) for k in range(1, n): c = U2jinv.taylor(x, 0, k).coefficient(x^k) U2jinv -= c*(jinv^k) coeff = U2jinv.taylor(x, 0, n).coefficient(x^n) return Integer(coeff).valuation(2) # Robin Visser, Jul 29 2023 CROSSREFS Cf. A000521, A007814, A344014, A344016, A344017. Sequence in context: A199129 A257942 A063244 * A281813 A374224 A063102 Adjacent sequences: A344012 A344013 A344014 * A344016 A344017 A344018 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 17 2021 EXTENSIONS More terms from Robin Visser, Jul 29 2023 STATUS approved

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Last modified August 11 12:11 EDT 2024. Contains 375069 sequences. (Running on oeis4.)