A392092 a(n+1) = a(n) + 2*d(a(n)) if s(a(n)) <= a(n), else 2*a(n) - s(a(n)), with a(1) = 2; d(k) is the number of divisors of k A000005 and s(k) is the aliquot sum of k A001065.

2, 6, 14, 22, 30, 18, 15, 23, 27, 35, 43, 47, 51, 59, 63, 75, 87, 95, 103, 107, 111, 119, 127, 131, 135, 151, 155, 163, 167, 171, 183, 191, 195, 211, 215, 223, 227, 231, 247, 255, 271, 275, 287, 295, 303, 311, 315, 339, 347, 351, 367, 371, 379, 383, 387, 399

Offset

1,1

Comments

The sequence becomes periodic starting from a(900).

Links

Adam Karol Drażyk, Table of n, a(n) for n = 1..2000

Formula

a(n+1) = if s(a(n)) <= a(n) then a(n) + 2*d(a(n)) else 2*a(n) - s(a(n)), where s(k) is A001065(k) and d(k) is A000005(k).

Example

Starting with a(1) = 2.
Sum of proper divisors of 2 is less than 2, so 2 + 2 * d(2) = 2 + 2 * 2 = 6. So a(2) = 6.
Sum of proper divisors of 6 is equal to 6, so 6 + 2 * d(6) = 6 + 2 * 4 = 14. So a(3) = 14
Sum of proper divisors of 14 is less than 14, so 14 + 2 * d(14) = 14 + 2 * 4 = 22. So a(4) = 22.
Sum of proper divisors of 22 is less than 22, so 22 + 2 * d(22) = 22 + 2 * 4 = 30. So a(5) = 30.
Sum of proper divisors of 30 is greater than 30, so 2 * 30 - s(30) = 2 * 30 - 42 = 18, where s(n) is the sum of proper divisors of n. So a(6) = 18.

Mathematica

NestWhileList[If[DivisorSigma[1, #] <= 2*#, # + 2*DivisorSigma[0, #], 3*# - DivisorSigma[1, #]] &, 2, Unequal, All]

Crossrefs

Cf. A000005, A001065, A394060 (different initial values).

Sequence in context: A101572 A080766 A262506 * A228649 A268641 A162796

Adjacent sequences: A392089 A392090 A392091 * A392093 A392094 A392095

Keyword

nonn

Author

Adam Karol Drażyk, Mar 06 2026

Status

approved