A306313 Numbers such that the product of their digits is equal to 10 times the sum of their prime factors, without multiplicity.

1584, 5616, 7452, 8256, 15698, 16956, 18525, 25662, 28512, 34935, 35152, 35275, 35581, 35748, 36584, 46225, 47265, 47594, 51842, 52374, 54479, 55223, 55348, 58432, 65712, 73125, 93875, 118465, 151632, 153615, 154462, 159712, 161785, 172577, 176225, 178754, 182596

Offset: 1

Author

Paolo P. Lava, Feb 06 2019

Keywords

• nonn
• base
• easy

Comments

Similar to Rhonda numbers (A099542) where the multiplicity of the prime factors is taken into account.

Examples

			1584 = 2^4*3^2*11 and 1*5*8*4 = 160 = 10*(2+3+11).
		

Crossrefs

Cf. A099542.

Programs

Maple

with(numtheory): select(n->convert(convert(n,base,10),`*`)=10*add(k,k=factorset(n)),[$1..120000]);

Mathematica

Select[Range[2*10^5], Times @@ IntegerDigits[#] == 10 Total[FactorInteger[#][[All, 1]] ] &] (* Michael De Vlieger, Feb 15 2019 *)