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 A046358 Composite numbers divisible by the palindromic sum of their prime factors (counted with multiplicity). 5
 4, 16, 27, 308, 440, 528, 594, 627, 1122, 1276, 3432, 3861, 4070, 4543, 5445, 5808, 6248, 6534, 7881, 8085, 8096, 9108, 9306, 9702, 11550, 13860, 14784, 16500, 16632, 17556, 18711, 19800, 19866, 20900, 21091, 21120, 22275, 22308, 23463, 23474 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..1000 EXAMPLE 1122 = 2 * 3 * 11 * 17 -> Sum of factors is palindrome 33 -> 1122 / 33 = 34 exactly. MAPLE 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: filter:= proc(n) local f; if n = 1 or isprime(n) then return false fi; f:= add(t[1]*t[2], t=ifactors(n)[2]); f = revdigs(f) and n mod f = 0 end proc: select(filter, [\$1..24000]); # Robert Israel, Aug 12 2014 MATHEMATICA palQ[n_]:= Reverse[x=IntegerDigits[n]] == x; Select[Range[4, 23480], !PrimeQ[#] && palQ[y=Total[Times@@@FactorInteger[#]]] && IntegerQ[#/y]&](* Jayanta Basu, Jun 05 2013 *) PROG (Python) from sympy import isprime, factorint 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 (PARI) rev(n)=my(r=""); d=digits(n); for(i=1, #d, r=concat(Str(d[i]), r)); return(eval(r)) sumfact(n)=my(v=Vec(factor(n))); p=0; for(j=1, #v[1], p+=v[1][j]*v[2][j]); return(p) forcomposite(n=1, 10^5, if(rev(sumfact(n))==sumfact(n)&&n%sumfact(n)==0, print1(n, ", "))) \\ Derek Orr, Aug 12 2014 CROSSREFS Cf. A046359, A046360. Sequence in context: A097374 A257309 A271936 * A046366 A227609 A219338 Adjacent sequences: A046355 A046356 A046357 * A046359 A046360 A046361 KEYWORD nonn,base AUTHOR Patrick De Geest, Jun 15 1998 EXTENSIONS Definition, offset and a(24) corrected by Chai Wah Wu, Aug 12 2014 STATUS approved

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Last modified September 10 03:08 EDT 2024. Contains 375770 sequences. (Running on oeis4.)