A143992 Numbers n such that the sum of the prime factors of n (counted with multiplicity) is a proper substring of n.

18, 144, 150, 168, 175, 198, 220, 230, 242, 246, 255, 322, 366, 444, 624, 1166, 1243, 1323, 1330, 1331, 1462, 1480, 1530, 1992, 2187, 2230, 2240, 2406, 2436, 2625, 2650, 2673, 2730, 2744, 2808, 2925, 3024, 3125, 3182, 3264, 3286, 3366, 3388, 3420, 3484

Offset

1,1

Comments

"Proper" is needed in the definition to exclude 4 and all primes.

Links

Table of n, a(n) for n=1..45.

Example

a(3)=144=2*2*2*2*3*3 and 2+2+2+2+3+3=14 and 14 is a substring of 144.

Mathematica

pfQ[n_]:=Module[{x=Total[Times@@@FactorInteger[n]], idx}, idx=IntegerDigits[x]; MemberQ[Partition[IntegerDigits[n], Length[idx], 1], idx]&&x!=n]
Select[Range[0, 3500], pfQ]  (* Harvey P. Dale, Feb 09 2011 *)

Prog

(Python)
from sympy import factorint, isprime
A143992_list = [n for n in range(2, 10**6) if n != 4 and not isprime(n) and str(sum(a*b for a, b in factorint(n).items())) in str(n)] # Chai Wah Wu, Aug 14 2021

Crossrefs

Sequence in context: A231951 A126513 A232820 * A127408 A008452 A126900

Adjacent sequences: A143989 A143990 A143991 * A143993 A143994 A143995

Keyword

base,nonn

Author

Gil Broussard, Sep 07 2008

Extensions

Corrected by Harvey P. Dale, Feb 09 2011

Status

approved