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

1,1

Comments

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

Links

Table of n, a(n) for n=1..37.

Example

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

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 *)

Crossrefs

Cf. A099542.

Sequence in context: A222164 A242539 A224945 * A053170 A237916 A159211

Adjacent sequences: A306310 A306311 A306312 * A306314 A306315 A306316

Keyword

nonn,base,easy

Author

Paolo P. Lava, Feb 06 2019

Status

approved