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
Keywords
Examples
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 +...
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..1000
Programs
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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
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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 *) -
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),", "))
Comments