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A219224 G.f.: exp( Sum_{n>=1} A005063(n)*x^n/n ), where A005063(n) = sum of squares of primes dividing n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Euler transform of A061397. - Peter Luschny, Nov 21 2022
LINKS
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
Sequence in context: A009097 A210194 A210755 * A265532 A112858 A161960
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 15 2012
STATUS
approved

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Last modified February 24 05:54 EST 2024. Contains 370294 sequences. (Running on oeis4.)