

A143992


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


0



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
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OFFSET

1,1


COMMENTS

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


LINKS



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]


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



KEYWORD

base,nonn


AUTHOR



EXTENSIONS

Corrected by Harvey P. Dale, Feb 09 2011


STATUS

approved



