A073396 The number n equals the product of two numbers: sums of prime factors of n, with and without repetition.

16, 27, 150

Offset: 1

Author

Reinhard Zumkeller, Jul 30 2002

Keywords

• nonn
• full
• fini
• bref

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

Examples

			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.
		

Links

• Max Alekseyev, Proof of finiteness of A073396, SeqFan Mailing List, May 4, 2013.

Crossrefs

Cf. A008472, A001414.

Programs

Mathematica

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

Formula

a(n) = A073395(a(n)).

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

Extensions

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