This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005063 Sum of squares of primes dividing n. 23
 0, 4, 9, 4, 25, 13, 49, 4, 9, 29, 121, 13, 169, 53, 34, 4, 289, 13, 361, 29, 58, 125, 529, 13, 25, 173, 9, 53, 841, 38, 961, 4, 130, 293, 74, 13, 1369, 365, 178, 29, 1681, 62, 1849, 125, 34, 533, 2209, 13, 49, 29, 298, 173, 2809, 13, 146, 53, 370, 845, 3481, 38, 3721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA Additive with a(p^e) = p^2. G.f.: Sum_{k>=1} prime(k)^2*x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Dec 24 2016 From Antti Karttunen, Jul 11 2017: (Start) a(n) = A005066(n) + 4*A059841(n). a(n) = A005079(n) + A005083(n) + 4*A059841(n). a(n) = A005071(n) + A005075(n) + 9*A079978(n). (End) Dirichlet g.f.: primezeta(s-2)*zeta(s). - Benedict W. J. Irwin, Jul 11 2018 MAPLE A005063 := proc(n)         add(d^2, d= numtheory[factorset](n)) ; end proc; seq(A005063(n), n=1..40) ; # R. J. Mathar, Nov 08 2011 MATHEMATICA a[n_] := Total[FactorInteger[n][[All, 1]]^2]; a[1]=0; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Mar 20 2017 *) Array[DivisorSum[#, #^2 &, PrimeQ] &, 61] (* Michael De Vlieger, Jul 11 2017 *) PROG (PARI) a(n)=local(fm, t); fm=factor(n); t=0; for(k=1, matsize(fm)[1], t+=fm[k, 1]^2); t \\ Franklin T. Adams-Watters, May 03 2009 (Scheme) (define (A005063 n) (if (= 1 n) 0 (+ (A000290 (A020639 n)) (A005063 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017 (Python) from sympy import primefactors def a(n): return sum([p**2 for p in primefactors(n)]) print map(a, xrange(1, 101)) # Indranil Ghosh, Jul 11 2017 CROSSREFS Cf. A000290, A005064, A005065, A005066, A005071, A005075, A005079, A005083, A008472, A059841, A079978. Cf. A067666, A081403, A048261. - Franklin T. Adams-Watters, May 03 2009 Sequence in context: A210966 A300516 A178147 * A235323 A078615 A197863 Adjacent sequences:  A005060 A005061 A005062 * A005064 A005065 A005066 KEYWORD nonn AUTHOR EXTENSIONS More terms from Franklin T. Adams-Watters, May 03 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 19 03:31 EDT 2019. Contains 328211 sequences. (Running on oeis4.)