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

1,1

Comments

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

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A130863 A070114 A070132 * A043218 A039395 A043998

Adjacent sequences: A280908 A280909 A280910 * A280912 A280913 A280914

Keyword

nonn,base,easy

Author

Ilya Gutkovskiy, Jan 10 2017

Status

approved