|
|
A301855
|
|
Number of divisors d|n such that no other divisor of n has the same Heinz weight A056239(d).
|
|
13
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
EXAMPLE
|
The a(24) = 4 special divisors are 1, 2, 12, 24.
|
|
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}]
|
|
PROG
|
(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
|
|
CROSSREFS
|
Cf. A000712, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301830, A301854, A301855, A301856.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|