A111073 Numbers n such that the sum of the smallest and largest prime factors of n divides n.

4, 8, 16, 32, 64, 126, 128, 252, 256, 378, 390, 504, 512, 630, 756, 780, 798, 882, 1008, 1024, 1134, 1150, 1170, 1260, 1512, 1560, 1596, 1764, 1890, 1950, 2016, 2046, 2048, 2268, 2300, 2340, 2394, 2520, 2646, 2730, 2886, 3024, 3120, 3150, 3192, 3402, 3450

Offset

1,1

Comments

All terms are even. - Harvey P. Dale, Sep 03 2015

Powers of 2 and numbers of the form 2 * p * (p + 2) * k where p is prime, p+2 isn't and k > 0 is p-smooth. - David A. Corneth, Sep 28 2019

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Example

126 = 2*3^2*7, with smallest and largest prime factors 2 and 7, sum = 9, and 126 is divisible by 9; so 126 is in the sequence.

Mathematica

slpdQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]}, Divisible[n, Total[ {First[f], Last[f]}]]]; Select[Range[4000], slpdQ] (* Harvey P. Dale, Sep 03 2015 *)

Prog

(PARI) lista(n) = {for (i=2, n, my(fac = factor(i), s = fac[1, 1] + fac[matsize(fac)[1], 1]); if (i % s == 0, print1(i, ", ")); ); } \\ Michel Marcus, May 18 2013

Crossrefs

Sequence in context: A108569 A342868 A196875 * A298807 A353500 A005934

Adjacent sequences: A111070 A111071 A111072 * A111074 A111075 A111076

Keyword

easy,nonn

Author

Joseph L. Pe, Oct 10 2005

Status

approved