A071192 -id:A071192 - cp's OEIS frontend

A071191 Least m>n such that the number of prime factors of m and n differ at most by 1.

2, 3, 4, 5, 6, 7, 9, 9, 10, 11, 13, 14, 14, 15, 17, 18, 19, 20, 21, 21, 22, 23, 25, 27, 26, 27, 28, 30, 31, 33, 33, 36, 34, 35, 37, 40, 38, 39, 41, 42, 43, 44, 46, 45, 46, 47, 49, 54, 50, 51, 52, 54, 55, 56, 57, 60, 58, 59, 61, 63, 62, 63, 65

Offset: 1

Reinhard Zumkeller, May 15 2002

nonn

abs(A001222(a(n)) - A001222(n)) <= 1.

			a(11) = 13 as 11 has one prime factor (counted with multiplicity) and 13 has 1 prime factor (counted with multiplicity), 13 the smallest number m > 11 such that the number of prime factors of m and 11 differ by at most 1. - _David A. Corneth_, Feb 23 2024

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A071192, A071193.

a(n) = {
	my(b = bigomega(n));
	for(i = n + 1, oo,
		if(abs(bigomega(i)-b) <= 1,
			return(i)
		)
	)
} \\ David A. Corneth, Feb 23 2024

A071193 Least m > n such that bigomega(m) != bigomega(n), where bigomega(n) = A001222(n).

Original entry on oeis.org

2, 4, 4, 5, 6, 7, 8, 9, 11, 11, 12, 13, 14, 16, 16, 17, 18, 19, 20, 21, 23, 23, 24, 25, 27, 27, 29, 29, 30, 31, 32, 33, 36, 36, 36, 37, 38, 40, 40, 41, 42, 43, 44, 46, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 59, 60, 61, 62, 63, 64

Offset: 1

Reinhard Zumkeller, May 15 2002

nonn

abs(A001222(a(n)) - A001222(n)) >= 1.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A001222, A071192, A071191.

Array[(k = #1; While[PrimeOmega[k] == #2, k++]; k) & @@ {#, PrimeOmega[#]} &, 64] (* Michael De Vlieger, Feb 23 2024 *)

A382229 a(0) = 1; thereafter a(n) is the next larger number that compared to the previous term differs by +-1 in the number of prime factors counted with multiplicity.

Original entry on oeis.org

1, 2, 4, 5, 6, 7, 9, 11, 14, 17, 21, 23, 25, 27, 33, 37, 38, 41, 46, 47, 49, 50, 51, 52, 54, 63, 65, 66, 69, 70, 74, 75, 77, 78, 81, 92, 93, 97, 106, 107, 111, 113, 115, 116, 118, 124, 126, 130, 132, 138, 140, 147, 150, 153, 155, 157, 158, 163, 166, 167, 169, 170, 177, 179, 183, 186

Offset: 0

Gordon Hamilton, Mar 19 2025

nonn

a(n+1) is the least integer k > a(n) such that abs(bigomega(k) - bigomega(a(n))) = 1.

Do an infinite number of primes appear in the sequence?

			Example: 52 = 2*2*13 is a term. 53 is not a term because it has -2 prime factors compared to 52. 54 = 2*3*3*3 is a term because it has +1 factor compared to 52. 55 = 5*11 is not a term because it has -2 factors compared to 54. 56 is not a term because it has the same number of factors as 54.

Cf. A001222 (bigomega), A071192.

lista(n)={my(L=List(), p=0, k=1); while(#LAndrew Howroyd, Mar 20 2025

a(n) = A071192(a(n-1)). - Pontus von Brömssen, Mar 21 2025

cp's OEIS Frontend

A071191 Least m>n such that the number of prime factors of m and n differ at most by 1.

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A071193 Least m > n such that bigomega(m) != bigomega(n), where bigomega(n) = A001222(n).

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A382229 a(0) = 1; thereafter a(n) is the next larger number that compared to the previous term differs by +-1 in the number of prime factors counted with multiplicity.

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