A300893 L.g.f.: log(Product_{k>=1} (1 + x^k)/(1 + x^prime(k))) = Sum_{n>=1} a(n)*x^n/n.

1, -1, 1, 3, 1, 5, 1, 3, 10, 9, 1, 9, 1, 13, 16, 3, 1, 14, 1, 13, 22, 21, 1, 9, 26, 25, 37, 17, 1, 30, 1, 3, 34, 33, 36, 18, 1, 37, 40, 13, 1, 40, 1, 25, 70, 45, 1, 9, 50, 34, 52, 29, 1, 41, 56, 17, 58, 57, 1, 34, 1, 61, 94, 3, 66, 60, 1, 37, 70, 58, 1, 18, 1, 73, 116, 41, 78, 70, 1, 13, 118, 81, 1, 44, 86

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} A018252(k)*x^A018252(k)/(1 + x^A018252(k)).

a(n) = 1 if n is an odd prime or 1 (A006005).

Example

L.g.f.: L(x) = x - x^2/2 + x^3/3 + 3*x^4/4 + x^5/5 + 5*x^6/6 + x^7/7 + 3*x^8/8 + 10*x^9/9 + 9*x^10/10 + ...
exp(L(x)) = 1 + x + x^4 + x^5 + x^6 + x^7 + x^8 + 2*x^9 + 3*x^10 + ... + A096258(n)*x^n + ...

Mathematica

nmax = 85; Rest[CoefficientList[Series[Log[Product[(1 + x^k)/(1 + x^Prime[k]), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]
nmax = 85; Rest[CoefficientList[Series[Sum[Boole[!PrimeQ[k]] k x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
Table[DivisorSum[n, (-1)^(n/# + 1) # &, !PrimeQ[#] &], {n, 85}]

Crossrefs

Cf. A006005, A018252, A023890, A096258, A300852.

Sequence in context: A274532 A254765 A372625 * A325249 A352453 A208239

Adjacent sequences: A300890 A300891 A300892 * A300894 A300895 A300896

Keyword

sign

Author

Ilya Gutkovskiy, Mar 14 2018

Status

approved