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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A036346, A046346.

Sequence in context: A144797 A173746 A095803 * A032464 A171381 A334083

Adjacent sequences: A036342 A036343 A036344 * A036346 A036347 A036348

Keyword

nonn

Author

Patrick De Geest, Dec 15 1998

Extensions

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

Status

approved