A317927 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A005187.

1, 3, 2, 19, 4, 2, 11, 63, 6, 3, 19, 13, 23, 17, 5, 867, 16, 4, 35, 5, 17, 25, 21, 11, 31, 29, 13, 113, 27, 13, 57, 3069, 13, 9, 23, 25, 71, 41, 14, 69, 79, 33, 41, 169, 9, 25, 89, 615, 259, 53, 17, 197, 51, 25, 29, 389, 20, 31, 113, 59, 117, 67, 10, 22199, 18, 14, 131, 31, 51, 71, 69, 11, 143, 77, 22, 281, 91, 35, 153, 489, 71, 85, 81, 151, 19

Offset

1,2

Comments

The first negative term is a(330) = -21.

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) * (A005187(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

Prog

(PARI)
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A317927perA317928(n) = if(1==n, n, (A005187(n)-sumdiv(n, d, if((d>1)&&(d<n), A317927perA317928(d)*A317927perA317928(n/d), 0)))/2);
A317927(n) = numerator(A317927perA317928(n));
(PARI)
\\ Memoized implementation:
memo = Map();
A317927perA317928(n) = if(1==n, n, if(mapisdefined(memo, n), mapget(memo, n), my(v = (A005187(n)-sumdiv(n, d, if((d>1)&&(d<n), A317927perA317928(d)*A317927perA317928(n/d), 0)))/2); mapput(memo, n, v); (v)));

Crossrefs

Cf. A005187, A317928 (denominators).

Cf. also A297111, A300244, A299151, A317931.

Sequence in context: A185447 A317831 A078073 * A075568 A366377 A057026

Adjacent sequences: A317924 A317925 A317926 * A317928 A317929 A317930

Keyword

sign,frac

Author

Antti Karttunen, Aug 11 2018

Status

approved