A374793 -id:A374793 - cp's OEIS frontend

A385375 Numbers k that can't be partitioned into tau(k) distinct parts.

2, 4, 6, 8, 12, 18, 20, 24, 30, 36, 48, 60, 72, 120

Offset: 1

Graph
List
Refs
Listen
History
Text
Internal format

Felix Huber, Jul 11 2025

nonn
fini
full

Numbers k for which k < A000217(tau(k)).

To partition k into tau(k) distinct parts, k >= tau(k)*(tau(k) + 1)/2. According to A374793, k > tau(k)^2 > tau(k)*(tau(k) + 1)/2 for k > 1260. The sequence is therefore finite and contains 14 terms.

			6 is a term because there is no partition of 6 into tau(6) = 4 distinct parts.

Cf. A000005, A000217, A374793, A385374.

with(NumberTheory):
A385375:=proc(K)
    local k,l;
    l:=[];
    for k from 1 to K do
        if tau(k)*(tau(k)+1)/2>k then
            l:=[op(l),k];
        end if;
    end do;
    return op(l);
end proc:
A385375(1260);

s={};Do[t=DivisorSigma[0,k];If[NoneTrue[Length/@Union/@IntegerPartitions[k,{t}],#==t&],AppendTo[s,k]],{k,72}];s (* James C. McMahon, Jul 24 2025 *)

cp's OEIS Frontend

A385375 Numbers k that can't be partitioned into tau(k) distinct parts.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica