

A073396


The number n equals the product of two numbers: sums of prime factors of n, with and without repetition.


3




OFFSET

1,1


COMMENTS

Numbers n such that n = A008472(n)*A001414(n) (= sum of distinct prime factors of n, times sum of prime factors of n with repetition).  M. F. Hasler, May 05 2013


LINKS

Table of n, a(n) for n=1..3.
Max Alekseyev, Proof of finiteness of A073396, SeqFan Mailing List, May 4, 2013.


FORMULA

a(n) = A073395(a(n)).
A073396 = { n  n = A008472(n)*A001414(n) }.  M. F. Hasler, May 05 2013


EXAMPLE

A073395(150) = A073395(2*3*5*5) = A008472(2*3*5*5)*A001414(2*3*5*5) = (2+3+5)*(2+3+5+5) = 10*15 = 150, therefore 150 is a term.


MATHEMATICA

okQ[n_] := n>1 && With[{f = FactorInteger[n]}, n == Total[Times @@@ f]* Total[f[[All, 1]]]];
Select[Range[1000], okQ] (* JeanFrançois Alcover, Apr 06 2021 *)


CROSSREFS

Cf. A008472, A001414.
Sequence in context: A280935 A067650 A123963 * A338093 A302553 A300132
Adjacent sequences: A073393 A073394 A073395 * A073397 A073398 A073399


KEYWORD

nonn,full,fini,bref


AUTHOR

Reinhard Zumkeller, Jul 30 2002


EXTENSIONS

Proof that there are no further terms added by Max Alekseyev, May 04 2013


STATUS

approved



