A050690 -id:A050690 - cp's OEIS frontend

A050689 Composites whose sum of digits equals number of its prime factors, with multiplicity.

12, 30, 32, 40, 102, 220, 240, 500, 600, 1002, 1012, 1104, 1152, 1210, 1320, 1500, 2001, 2002, 2020, 2040, 2120, 2240, 2300, 3010, 3040, 3300, 4032, 4100, 4320, 5100, 5200, 6400, 7000, 7200, 10001, 10002, 10011, 10030, 10040, 10080, 10140, 10220, 10304, 10800

Offset: 1

Patrick De Geest, Aug 15 1999

The sequence is infinite because there are infinitely many primes whose sum of digits is odd (see related comment in A119450). Let p be one of them, and let k be its digital sum. Then p*10^((k-1)/2) is a term. For example, 41*10^2 is a term. - Metin Sariyar, May 30 2020

			2002 is a term since 2+0+0+2 = 4, and 2002 = 2*7*11*13 has 4 prime factors.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 322 terms from Michael Turniansky)

Cf. A050690, A057531, A057532, A070274, A070275, A063737, A067077, A119450.

Select[Range[10300],!PrimeQ[#]&&PrimeOmega[#]==Total[IntegerDigits[#]]&] (* Jayanta Basu, May 30 2013 *)

isok(n) = sumdigits(n) == bigomega(n); \\ Michel Marcus, Feb 13 2017

from sympy import factorint
def ok(n): return 1 < sum(map(int, str(n))) == sum(factorint(n).values())
print([k for k in range(11000) if ok(k)]) # Michael S. Branicky, Dec 30 2021

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.

Original entry on oeis.org

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

Ilya Gutkovskiy, Jan 10 2017

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

			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.

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

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

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

cp's OEIS Frontend

A050689 Composites whose sum of digits equals number of its prime factors, with multiplicity.

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