A380866 a(n) is the least m > 0 such that sigma(m) - 2m = A140863(n).

18, 196, 100, 36, 15376, 162, 1352, 72, 968, 200, 392, 13456, 144, 8450, 1032256, 400, 119072, 324, 8464, 288, 1936, 5776, 2704, 4624, 111392, 450, 800, 1458, 9604, 2450, 1568, 882, 2500, 576, 648, 89888, 3872, 5408, 1600, 70688, 2178, 9248, 11552, 11025, 59168, 53792, 3136, 16928, 1152, 900, 43808, 26912, 3042, 30752

Offset: 1

Author

M. F. Hasler, Mar 10 2025

Keywords

• nonn

Comments

A140863 lists odd numbers k > 0 for which there is a solution to sigma(x) = 2x + k; this sequence lists the smallest such solution.

a(44) = 11025 = 105^2 is the first odd term of this sequence.

Examples

			The smallest (positive) odd number that can occur as abundance A033880 of some abundant number (A005101) is A140863(1) = A033880(18) = 3. Since n = 18 is the least index where 3 appears in A033880, a(1) = 18.
		

Crossrefs

Cf. A000203 (sigma), A033880 (abundance: sigma(n)-2n).

Cf. A140863 (odd numbers k = A033880(m) for some m).

Programs

PARI

A380866(n, k=A140863[n])=for(m=1,oo,sigma(m)-2*m==k && return(m)) \\ If the k-value is given as 2nd argument, the first argument is ignored. Otherwise, the vector or list A140863 must be defined up to the n-th element.

Formula

a(n) = (A000203(a(n)) - A140863(n))/2.