A281782 Numbers n such that sum of prime power divisors of n > sum of prime power divisors of m for all m < n.

2, 3, 4, 7, 8, 16, 27, 32, 64, 121, 125, 128, 243, 256, 512, 729, 1024, 2048, 4096, 6561, 8192, 15625, 16384, 32761, 32768, 59049, 65536, 117649, 130321, 131072, 177147, 262144, 524287, 524288, 1048576, 1594323, 1953125, 2097152, 4194304, 8388608

Offset: 1

Author

Ilya Gutkovskiy, Apr 14 2017

Keywords

• nonn

Comments

Numbers n such that A023889(n) > A023889(m) for all m < n.

Numbers n such that Sum_{p^k|n, p prime, k>=1} p^k > Sum_{p^k|m, p prime, k>=1} p^k for all m < n.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..65
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A002093, A002182, A023889, A034090, A174572, A246655, A280013.

Programs

Mathematica

mx = 0; t = {}; Do[u = DivisorSum[n, # &, PrimePowerQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 8500000}]; t