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

Author

T. D. Noe, Apr 08 2014

Keywords

• nonn

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

Crossrefs

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

Cf. A228450 (deficient numbers with increasing abundancy).

Programs

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

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