A074256 - OEIS

%I #23 Sep 18 2024 11:23:25

%S 2,242,1323,3200,13050,30000,42432,132300,426205,442244,620425,665353,

%T 1261645,1306254,1453032,1461363,1523340,1523466,2025012,2105334,

%U 2134350,2205102,2613504,2713421,3005264,3312400,3314520,3432000

%N Numbers k such that the sum of factorials of the digits of k equals the sum of the primes from the smallest prime factor of k to the largest prime factor of k.

%C Numbers k such that A061602(k) = A074036(k). - _Andrew Howroyd_, Sep 18 2024

%e 242 = 2*11^2 and 2+3+5+7+11 = 28 and 2!+4!+2! = 28.

%t okQ[n_]:=Module[{ifn=Transpose[FactorInteger[n]][[1]]}, Total[Prime[ Range[ PrimePi[ Min[ifn]], PrimePi[Max[ifn]]]]]==Total[IntegerDigits[n]!]]; Select[Range[ 2,3500000],okQ]  (* _Harvey P. Dale_, Apr 21 2011 *)

%o (PARI) isok(n)={my(d=digits(n), s=sum(k=1, #d, d[k]!), f=factor(n)[,1]); if(#f, forprime(p=f[1], f[#f], s-=p)); s==0} \\ _Andrew Howroyd_, Sep 18 2024

%Y Cf. A061602, A074036.

%K nonn,base

%O 1,1

%A _Jason Earls_, Sep 20 2002

%E More terms from _Michel ten Voorde_, Jun 20 2003

%E More terms from _Sam Alexander_, Feb 28 2005

%E Offset changed by _Andrew Howroyd_, Sep 18 2024