A280911 Numbers n such that sum of decimal digits of n equals number of prime divisors of n counted with multiplicity and sum of distinct decimal digits of n equals number of distinct primes dividing n.

30, 102, 1002, 1012, 1210, 2001, 2120, 3010, 10002, 10030, 20001, 20112, 20120, 100012, 100030, 101020, 102010, 110020, 110120, 120001, 121120, 200001, 200120, 211100, 221120, 230010, 300010, 320320, 400010, 400140, 1000002, 1000012, 1000140, 1000230, 1001020, 1003002, 1004010, 1010120, 1011300, 1013310, 1021100

Offset: 1

Author

Ilya Gutkovskiy, Jan 10 2017

Keywords

• nonn
• base
• easy

Comments

Numbers n such that A007953(n) = A001222(n) and A217928(n) = A001221(n).

Examples

			20112 is in the sequence because 20112 = 2^4*3*419  (6 prime factors, 3 distinct), 2 + 0 + 1 + 1 + 2 = 6 and 2 + 0 + 1 = 3.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digit Sum
• Eric Weisstein's World of Mathematics, Prime Factor
• Eric Weisstein's World of Mathematics, Distinct Prime Factors

Crossrefs

Cf. A001221, A001222, A007953, A050689, A050690, A057531, A217928.

Programs

Mathematica

Select[Range[1100000], Total[IntegerDigits[#1]] == PrimeOmega[#1] && Total[Union[IntegerDigits[#1]]] == PrimeNu[#1] &]