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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 xrange(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 July 24 05:18 EDT 2017. Contains 289717 sequences.