A301855 Number of divisors d|n such that no other divisor of n has the same Heinz weight A056239(d).

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 4, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 4, 3, 4, 4, 6, 2, 6, 2, 6, 4, 4, 4, 5, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 4, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 4, 2, 4, 4, 7, 4, 8, 2, 6, 4, 6, 2, 4, 2, 4, 6, 6, 4, 8, 2, 6, 5, 4, 2, 6, 4, 4, 4, 8, 2, 6, 4, 6, 4, 4, 4, 4, 2, 6, 6, 9, 2, 8, 2, 8, 8

Offset: 1

Author

Gus Wiseman, Mar 27 2018

Keywords

• nonn

Examples

			The a(24) = 4 special divisors are 1, 2, 12, 24.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000712, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301830, A301854, A301855, A301856.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
uqsubs[y_]:=Join@@Select[GatherBy[Union[Subsets[y]],Total],Length[#]===1&];
Table[Length[uqsubs[primeMS[n]]],{n,100}]

PARI

A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A301855(n) = if(1==n,n,my(m=Map(),w,s); fordiv(n,d,w = A056239(d); if(!mapisdefined(m, w, &s), mapput(m,w,Set([d])), mapput(m,w,setunion(Set([d]),s)))); sumdiv(n,d,(1==length(mapget(m,A056239(d)))))); \\ Antti Karttunen, Jul 01 2018

Extensions

More terms from Antti Karttunen, Jul 01 2018