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A036345 Divisible by its 'even' sum of prime factors (counted with multiplicity). 2

%I #24 Feb 18 2019 08:07:12

%S 2,4,16,30,60,70,72,84,220,240,256,286,288,308,378,440,450,476,528,

%T 540,560,576,594,624,646,648,728,800,884,900,960,1040,1056,1080,1160,

%U 1170,1248,1276,1404,1456,1496,1530,1748,1776,1798,1824,1976,2322,2408,2464

%N Divisible by its 'even' sum of prime factors (counted with multiplicity).

%H David A. Corneth, <a href="/A036345/b036345.txt">Table of n, a(n) for n = 1..10000</a> (terms a(n) for n = 2..1002 from Harvey P. Dale).

%e 646 = 2*17*19 so the sum of prime factors (with multiplicity) is 2+17+19 = 38 which is even and a divisor of 646 so 646 is in the sequence.

%t dspfQ[n_]:=Module[{spf=Total[Times@@@FactorInteger[n]]},EvenQ[spf] && Divisible[n,spf]]; Select[Range[4,2500,2],dspfQ] (* _Harvey P. Dale_, Oct 06 2011 *)

%o (PARI) is(n) = my(f = factor(n), s = sum(i = 1, #f~, f[i, 1] * f[i, 2])); s > 0 && s % 2 == 0 && n % s == 0 \\ _David A. Corneth_, Feb 07 2019

%Y Cf. A036346, A046346.

%K nonn

%O 1,1

%A _Patrick De Geest_, Dec 15 1998

%E Offset corrected and a(1) = 2 added by _Thomas Ordowski_, Feb 07 2019

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Last modified April 17 23:23 EDT 2024. Contains 371767 sequences. (Running on oeis4.)