A364700 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A364700

Numerators of coefficients in expansion of sqrt( Sum_{j>=1} x^prime(j) ).

1, 1, -1, 9, -37, 183, -565, 1081, -25453, 96427, -404927, 1279359, -12561457, 33077619, -194103389, 577222425, -25302548477, 74326953907, -423955653883, 1225808143651, -14456976876619, 42661352483945, -250437691682371, 741244373831663, -17624677238323753, 52507307961906687, -314022434935401067

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

The coefficients are 1, 1/2, -1/8, 9/16, -37/128, 183/256, -565/1024, 1081/2048, -25453/32768, ...

MATHEMATICA

nmax = 27; CoefficientList[Series[Sqrt[Sum[x^Prime[j], {j, 1, nmax}]], {x, 0, nmax}], x] // Numerator // Rest

CROSSREFS

The denominators appear to be A046161.

Cf. A000040, A001790, A010051, A073749.