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A317925 Numerators of rational valued sequence whose Dirichlet convolution with itself yields Euler's phi (A000010). 7
1, 1, 1, 7, 2, 1, 3, 25, 5, 1, 5, 7, 6, 3, 2, 363, 8, 5, 9, 7, 3, 5, 11, 25, 8, 3, 13, 21, 14, 1, 15, 1335, 5, 4, 6, 35, 18, 9, 6, 25, 20, 3, 21, 35, 5, 11, 23, 363, 33, 4, 8, 21, 26, 13, 10, 75, 9, 7, 29, 7, 30, 15, 15, 9923, 12, 5, 33, 7, 11, 3, 35, 125, 36, 9, 8, 63, 15, 3, 39, 363, 139, 10, 41, 21, 16, 21, 14, 125, 44, 5, 18, 77, 15, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A000010(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

A317925perA317926(n) = if(1==n, n, (eulerphi(n)-sumdiv(n, d, if((d>1)&&(d<n), A317925perA317926(d)*A317925perA317926(n/d), 0)))/2);

A317925(n) = numerator(A317925perA317926(n));

(PARI)

\\ Memoized implementation:

memo = Map();

A317925perA317926(n) = if(1==n, n, if(mapisdefined(memo, n), mapget(memo, n), my(v = (eulerphi(n)-sumdiv(n, d, if((d>1)&&(d<n), A317925perA317926(d)*A317925perA317926(n/d), 0)))/2); mapput(memo, n, v); (v)));

CROSSREFS

Cf. A000010, A317926 (denominators).

Cf. also A046643, A317831.

Sequence in context: A220862 A198229 A133362 * A010140 A222067 A154020

Adjacent sequences:  A317922 A317923 A317924 * A317926 A317927 A317928

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Aug 11 2018

STATUS

approved

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Last modified April 7 13:27 EDT 2020. Contains 333305 sequences. (Running on oeis4.)