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

1,2

Links

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

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.

Sequence in context: A355302 A084302 A289872 * A080256 A351394 A327527

Adjacent sequences: A301852 A301853 A301854 * A301856 A301857 A301858

Keyword

nonn

Author

Gus Wiseman, Mar 27 2018

Extensions

More terms from Antti Karttunen, Jul 01 2018

Status

approved