A301855 - OEIS

%I #9 Jul 02 2018 06:59:43

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A301855/b301855.txt">Table of n, a(n) for n = 1..65537</a>

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

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t uqsubs[y_]:=Join@@Select[GatherBy[Union[Subsets[y]],Total],Length[#]===1&];

%t Table[Length[uqsubs[primeMS[n]]],{n,100}]

%o (PARI)

%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }

%o 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

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 27 2018

%E More terms from _Antti Karttunen_, Jul 01 2018