A161946 Odd part of sum of unitary divisors of n.

1, 3, 1, 5, 3, 3, 1, 9, 5, 9, 3, 5, 7, 3, 3, 17, 9, 15, 5, 15, 1, 9, 3, 9, 13, 21, 7, 5, 15, 9, 1, 33, 3, 27, 3, 25, 19, 15, 7, 27, 21, 3, 11, 15, 15, 9, 3, 17, 25, 39, 9, 35, 27, 21, 9, 9, 5, 45, 15, 15, 31, 3, 5, 65, 21, 9, 17, 45, 3, 9, 9, 45, 37, 57, 13, 25, 3, 21, 5, 51, 41, 63, 21, 5, 27

Offset

1,2

Comments

Since a(n) < n for any odd n > 1, iterating this function always leads to 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

Multiplicative with a(p^e) = oddpart(p^e+1), where oddpart(n) = A000265(n) is the largest odd divisor of n.

Mathematica

Table[NestWhile[#/2 &, DivisorSum[n, # &, CoprimeQ[#, n/#] &], EvenQ@ # &], {n, 85}] (* Michael De Vlieger, Nov 23 2017 *)
a[n_] := Times @@ ((#/2^IntegerExponent[#, 2]) & /@ (1 + Power @@@ FactorInteger[n])); Array[a, 100] (* Amiram Eldar, Oct 26 2023 *)

Prog

(PARI) oddpart(n)=n/2^valuation(n, 2)
a(n)=local(fm, r); fm=factor(n); r=1; for(k=1, matsize(fm)[1], r*=oddpart(fm[k, 1]^fm[k, 2]+1)); r

Crossrefs

Cf. A000265, A161942, A034448, A151659.

Sequence in context: A356255 A152203 A340526 * A013597 A092131 A092099

Adjacent sequences: A161943 A161944 A161945 * A161947 A161948 A161949

Keyword

easy,mult,nonn

Author

Franklin T. Adams-Watters, Jun 22 2009

Status

approved