A074256 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.

2, 242, 1323, 3200, 13050, 30000, 42432, 132300, 426205, 442244, 620425, 665353, 1261645, 1306254, 1453032, 1461363, 1523340, 1523466, 2025012, 2105334, 2134350, 2205102, 2613504, 2713421, 3005264, 3312400, 3314520, 3432000

Offset: 1

Author

Jason Earls, Sep 20 2002

Keywords

• nonn
• base

Comments

Numbers k such that A061602(k) = A074036(k). - Andrew Howroyd, Sep 18 2024

Examples

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

Crossrefs

Cf. A061602, A074036.

Programs

Mathematica

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 *)

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

Extensions

More terms from Michel ten Voorde, Jun 20 2003

More terms from Sam Alexander, Feb 28 2005

Offset changed by Andrew Howroyd, Sep 18 2024