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 A358033 a(1) = 2; a(n) - a(n-1) = A093803(a(n-1)), the largest odd proper divisor of a(n-1). 0
 2, 3, 4, 5, 6, 9, 12, 15, 20, 25, 30, 45, 60, 75, 100, 125, 150, 225, 300, 375, 500, 625, 750, 1125, 1500, 1875, 2500, 3125, 3750, 5625, 7500, 9375, 12500, 15625, 18750, 28125, 37500, 46875, 62500, 78125, 93750, 140625, 187500, 234375, 312500, 390625, 468750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..47. FORMULA a(n+1) - a(n) = A056487(floor((n-2)/3)), for n > 2. This works because A056487(n+3) = A056487(n+2)*A056487(n+1)/A056487(n). - Thomas Scheuerle, Oct 26 2022 EXAMPLE a(1) = 2. a(2) = 3. The only proper divisor of 2 is 1; 2 + 1 = 3. a(3) = 4. The only proper divisor of 3 is 1; 3 + 1 = 4. ... a(8) = 15. a(9) = 20. Proper divisors of 15 are 1, 3, 5; largest odd proper divisor = 5; 15 + 5 = 20. PROG (Python) a_n = 2 result = [2] for n in range(30): temp = [] for i in range(1, a_n): if a_n % i == 0: if (i % 2 != 0) and (i != a_n): temp.append(i) result.append(a_n + max(temp)) a_n = a_n + max(temp) print(result) (PARI) f(n) = my(x=if(n==1, 1, n/factor(n)[1, 1])); x >> valuation(x, 2); \\ Michel Marcus, Oct 26 2022 lista(nn) = my(va = vector(nn)); va[1] = 2; for (n=2, nn, va[n] = va[n-1] + f(va[n-1]); ); va; \\ Michel Marcus, Oct 26 2022 CROSSREFS Cf. A093803, A000792 (with largest proper divisor instead). Cf. A027750, A038754, A056487, A356639. Sequence in context: A133463 A187550 A307818 * A057492 A178715 A018123 Adjacent sequences: A358030 A358031 A358032 * A358034 A358035 A358036 KEYWORD nonn,easy AUTHOR Eric Angelini and Gavin Lupo, Oct 25 2022 STATUS approved

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Last modified June 24 15:53 EDT 2024. Contains 373679 sequences. (Running on oeis4.)