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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 (list; graph; refs; listen; history; text; internal format)
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. Adams-Watters, Jun 22 2009

STATUS

approved

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Last modified February 24 13:13 EST 2021. Contains 341569 sequences. (Running on oeis4.)