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

2, 4, 16, 30, 60, 70, 72, 84, 220, 240, 256, 286, 288, 308, 378, 440, 450, 476, 528, 540, 560, 576, 594, 624, 646, 648, 728, 800, 884, 900, 960, 1040, 1056, 1080, 1160, 1170, 1248, 1276, 1404, 1456, 1496, 1530, 1748, 1776, 1798, 1824, 1976, 2322, 2408, 2464

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (terms a(n) for n = 2..1002 from Harvey P. Dale).

Crossrefs

Cf. A036346, A046346.

Programs

Mathematica

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 *)

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

Extensions

Offset corrected and a(1) = 2 added by Thomas Ordowski, Feb 07 2019