A386546 Numbers k >= 1 such that k = d(k) + d(k+1) + ... + d(k+r) for some r >= 0 where d(i) is the number of divisors of i (A000005).

1, 2, 6, 9, 12, 18, 21, 26, 28, 31, 43, 49, 52, 54, 73, 79, 91, 93, 95, 99, 102, 109, 111, 121, 122, 133, 153, 159, 175, 179, 185, 193, 197, 211, 215, 227, 231, 239, 241, 243, 271, 279, 286, 291, 295, 299, 301, 305, 309, 311, 313, 318, 324, 329, 339, 345

Offset: 1

Author

Ctibor O. Zizka, Jul 25 2025

Keywords

• nonn

Comments

r is from {0,0,1,2,2,3,4,5,5,6,8,9,9,13,13,13,16,15,15,...}.

Examples

			For k = 2: 2 = A000005(2) = 2, thus 2 is a term.
For k = 6: 6 = A000005(6) + A000005(7) = 4 + 2 = 6, thus 6 is a term.
		

Crossrefs

Cf. A000005.

Programs

Mathematica

q[k_] := Module[{s = 0, m = k}, While[s < k, s += DivisorSigma[0, m]; m++]; s == k]; Select[Range[350], q] (* Amiram Eldar, Jul 25 2025 *)