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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.
1
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
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] &]
KEYWORD
nonn,base,easy
AUTHOR
Ilya Gutkovskiy, Jan 10 2017
STATUS
approved