A046358 - OEIS

%I #25 Dec 07 2019 12:18:21

%S 4,16,27,308,440,528,594,627,1122,1276,3432,3861,4070,4543,5445,5808,

%T 6248,6534,7881,8085,8096,9108,9306,9702,11550,13860,14784,16500,

%U 16632,17556,18711,19800,19866,20900,21091,21120,22275,22308,23463,23474

%N Composite numbers divisible by the palindromic sum of their prime factors (counted with multiplicity).

%H Chai Wah Wu, <a href="/A046358/b046358.txt">Table of n, a(n) for n = 1..1000</a>

%e 1122 = 2 * 3 * 11 * 17 -> Sum of factors is palindrome 33 -> 1122 / 33 = 34 exactly.

%p revdigs:= proc(n) local L,nL; L:= convert(n,base,10); nL:= nops(L); add(L[i]*10^(nL-i),i=1..nL) end proc:

%p filter:= proc(n) local f;

%p if n = 1 or isprime(n) then return false fi;

%p f:= add(t[1]*t[2],t=ifactors(n)[2]);

%p f = revdigs(f) and n mod f = 0

%p end proc:

%p select(filter, [$1..24000]); # _Robert Israel_, Aug 12 2014

%t palQ[n_]:= Reverse[x=IntegerDigits[n]] == x; Select[Range[4, 23480], !PrimeQ[#] && palQ[y=Total[Times@@@FactorInteger[#]]] && IntegerQ[#/y]&](* _Jayanta Basu_, Jun 05 2013 *)

%o (Python)

%o from sympy import isprime, factorint

%o A046358 = [n for n in range(2,10**6) if not isprime(n) and not n % sum([p*e for p,e in factorint(n).items()]) and str(sum([p*e for p,e in factorint(n).items()])) == str(sum([p*e for p,e in factorint(n).items()]))[::-1]] # _Chai Wah Wu_, Aug 12 2014

%o (PARI)

%o rev(n)=my(r="");d=digits(n);for(i=1,#d,r=concat(Str(d[i]),r));return(eval(r))

%o sumfact(n)=my(v=Vec(factor(n)));p=0;for(j=1,#v[1],p+=v[1][j]*v[2][j]);return(p)

%o forcomposite(n=1,10^5,if(rev(sumfact(n))==sumfact(n)&&n%sumfact(n)==0,print1(n,", "))) \\ _Derek Orr_, Aug 12 2014

%Y Cf. A046359, A046360.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Jun 15 1998

%E Definition, offset and a(24) corrected by _Chai Wah Wu_, Aug 12 2014