cp's OEIS Frontend

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.

%I A280911 #8 Feb 16 2025 08:33:39
%S A280911 30,102,1002,1012,1210,2001,2120,3010,10002,10030,20001,20112,20120,
%T A280911 100012,100030,101020,102010,110020,110120,120001,121120,200001,
%U A280911 200120,211100,221120,230010,300010,320320,400010,400140,1000002,1000012,1000140,1000230,1001020,1003002,1004010,1010120,1011300,1013310,1021100
%N 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.
%C A280911 Numbers n such that A007953(n) = A001222(n) and A217928(n) = A001221(n).
%H A280911 Giovanni Resta, <a href="/A280911/b280911.txt">Table of n, a(n) for n = 1..10000</a>
%H A280911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>
%H A280911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%H A280911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%e A280911 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.
%t A280911 Select[Range[1100000], Total[IntegerDigits[#1]] == PrimeOmega[#1] && Total[Union[IntegerDigits[#1]]] == PrimeNu[#1] &]
%Y A280911 Cf. A001221, A001222, A007953, A050689, A050690, A057531, A217928.
%K A280911 nonn,base,easy
%O A280911 1,1
%A A280911 _Ilya Gutkovskiy_, Jan 10 2017