A219224 G.f.: exp( Sum_{n>=1} A005063(n)*x^n/n ), where A005063(n) = sum of squares of primes dividing n.

1, 0, 2, 3, 3, 11, 10, 26, 32, 51, 90, 117, 198, 283, 417, 610, 890, 1284, 1848, 2615, 3716, 5217, 7289, 10222, 14158, 19514, 26882, 36805, 50131, 68428, 92466, 125128, 168093, 225775, 302171, 402876, 536730, 711601, 942009, 1243513, 1638395, 2152828, 2823004

Offset

0,3

Comments

Euler transform of A061397. - Peter Luschny, Nov 21 2022

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + 2*x^2 + 3*x^3 + 3*x^4 + 11*x^5 + 10*x^6 + 26*x^7 + 32*x^8 +...
where
log(A(x)) = 4*x^2/2 + 9*x^3/3 + 4*x^4/4 + 25*x^5/5 + 13*x^6/6 + 49*x^7/7 + 4*x^8/8 + 9*x^9/9 + 29*x^10/10 + 121*x^11/11 + 13*x^12/12 + 169*x^13/13 + 53*x^14/14 + 34*x^15/15 +...+ A005063(n)*x^n/n +...

Maple

# The function EulerTransform is defined in A358369.
a := EulerTransform(n -> ifelse(isprime(n), n, 0)):
seq(a(n), n = 0..42); # Peter Luschny, Nov 21 2022

Mathematica

a[n_] := SeriesCoefficient[ Exp[ Sum[ DivisorSum[k, Boole[PrimeQ[#]] * #^2&] * x^k/k, {k, 1, n+1}]], {x, 0, n}]; Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Jul 11 2017, from PARI *)

Prog

(PARI) {a(n)=polcoeff(exp(sum(k=1, n+1, sumdiv(k, d, isprime(d)*d^2)*x^k/k)+x*O(x^n)), n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A000607, A005063, A220427, A061397.

Sequence in context: A009097 A210194 A210755 * A265532 A112858 A161960

Adjacent sequences: A219221 A219222 A219223 * A219225 A219226 A219227

Keyword

nonn

Author

Paul D. Hanna, Nov 15 2012

Status

approved