

A161946


Odd part of sum of unitary divisors of n.


2



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
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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 *)


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: A249100 A152203 A340526 * A013597 A092131 A092099
Adjacent sequences: A161943 A161944 A161945 * A161947 A161948 A161949


KEYWORD

easy,mult,nonn


AUTHOR

Franklin T. AdamsWatters, Jun 22 2009


STATUS

approved



