A240073 Deficient numbers k for which sigma(k), the sum of divisors of k, reaches a new maximum.

1, 2, 3, 4, 7, 8, 10, 14, 16, 21, 22, 26, 32, 44, 50, 52, 63, 64, 76, 92, 98, 105, 110, 124, 128, 136, 152, 170, 182, 184, 212, 225, 230, 232, 248, 256, 290, 296, 310, 315, 328, 344, 370, 376, 405, 410, 424, 470, 472, 484, 495, 512, 568, 584, 592, 632, 656

Offset

1,2

Comments

Every power of 2 appears. The deficient number k has sigma(k) < 2*k. In relation to the highly abundant numbers, these numbers might be termed highly deficient numbers.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Mathematica

t = {}; mn = 0; n = 0; While[Length[t] < 100, n++; d = DivisorSigma[1, n]; If[mn < d < 2*n, AppendTo[t, n]; mn = d]]; t

Prog

(PARI) lista(kmax) = {my(sigmax = 0, sig); for(k = 1, kmax, sig = sigma(k); if(sig < 2*k && sig > sigmax, sigmax = sig; print1(k, ", "))); } \\ Amiram Eldar, Apr 06 2024

Crossrefs

Cf. A002093 (highly abundant numbers), A005100 (deficient numbers).

Cf. A228450 (deficient numbers with increasing abundancy).

Sequence in context: A171781 A329395 A065294 * A332579 A357490 A333778

Adjacent sequences: A240070 A240071 A240072 * A240074 A240075 A240076

Keyword

nonn

Author

T. D. Noe, Apr 08 2014

Status

approved