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%I #33 Sep 27 2020 02:38:51
%S 0,4,9,8,25,13,49,12,18,29,121,17,169,53,34,16,289,22,361,33,58,125,
%T 529,21,50,173,27,57,841,38,961,20,130,293,74,26,1369,365,178,37,1681,
%U 62,1849,129,43,533,2209,25,98,54,298,177,2809,31,146,61,370,845,3481
%N Sum of squares of prime factors of n (counted with multiplicity).
%C 16 and 27 are fixed points, ... and see Rivera link. - _Michel Marcus_, Sep 19 2020
%H Charles R Greathouse IV, <a href="/A067666/b067666.txt">Table of n, a(n) for n = 1..10000</a>
%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_625.htm">Puzzle 625. Sum of squares of prime divisors</a>, The Prime Puzzles and Problems Connection.
%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_1019.htm">Puzzle 1019. Follow-up to Puzzle 625</a>, The Prime Puzzles and Problems Connection.
%F a(x*y) = a(x) + a(y); a(p^k) = k*p^2 for p prime.
%F Totally additive with a(p) = p^2.
%e a(2) = 2^2 = 4;
%e a(45) = a(3*3*5) = 3^2 + 3^2 + 5^2 = 43.
%t Join[{0},Table[Total[Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[ n]]^2],{n,2,60}]] (* _Harvey P. Dale_, Dec 24 2012 *)
%t Join[{0}, Table[Total[#[[1]]^2*#[[2]] & /@ FactorInteger[n]], {n, 2, 60}]] (* _Zak Seidov_, Apr 18 2013 *)
%o (PARI) a(n)=local(fm,t);fm=factor(n);t=0;for(k=1,matsize(fm)[1],t+=fm[k,1]^2*fm[k,2]);t \\ _Franklin T. Adams-Watters_, May 03 2009
%o (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]^2*f[k,2]); \\ _Michel Marcus_, Sep 19 2020
%Y Cf. A166319 (where a(n)<=n), A001222, A001414, A005063, A078137, A081403.
%K nonn
%O 1,2
%A _Henry Bottomley_, Feb 04 2002
%E Values through a(59) verified by _Franklin T. Adams-Watters_, May 03 2009
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