A112231 -id:A112231 - cp's OEIS frontend

A112233 A112231(n) + A112232(n).

2, 4, 5, 7, 7, 9, 11, 11, 13, 15, 15, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 36, 37, 38, 40, 42, 43, 44, 45, 47, 48, 50, 52, 53, 54, 55, 57, 57, 59, 60, 62, 63, 65, 67, 67, 69, 71, 72, 74, 74, 76, 77, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92, 94, 95, 96, 98

Offset: 1

Reinhard Zumkeller, Aug 29 2005

nonn

Cf. A112234, A112235.

A361761 a(n) = Product_{i=prime(n)..prime(n+1)} i.

Original entry on oeis.org

6, 60, 210, 55440, 1716, 742560, 5814, 4037880, 7866331200, 26970, 51889178880, 89927760, 74046, 184072680, 776881123200, 1719393207840, 215940, 4383026968320, 1562389080, 373176, 14609718723600, 3484127520, 34726953602880, 518607878946393600, 9505049400, 1061106

Offset: 1

Karl-Heinz Hofmann, Mar 23 2023

nonn

Winston de Greef, Table of n, a(n) for n = 1..10000

Cf. A006094, A061214, A072472, A112231, A361760.

a(n) = my(x=1); for(i=prime(n), prime(n+1), x*=i); x; \\ Michel Marcus, Mar 28 2023

from sympy import prod, sieve
def A361761(n): return prod(range(sieve[n],sieve[n+1]+1))

a(n) = A006094(n)*A061214(n).

A112232 Repeat each composite number in the sequence of natural numbers.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45

Offset: 1

Reinhard Zumkeller, Aug 29 2005

nonn

a(n) = A112233(n) - A112231(n);
a(n + A002808(n) - 1) = A002808(n),
a(n + A002808(n)) = A002808(n),
a(n + A002808(n) + 1) = A002808(n) + 1.

cp's OEIS Frontend

A112233 A112231(n) + A112232(n).

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A361761 a(n) = Product_{i=prime(n)..prime(n+1)} i.

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A112232 Repeat each composite number in the sequence of natural numbers.

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