A064909 -id:A064909 - cp's OEIS frontend

A064910 Smallest semiprime p*q such that q >= p and q mod p = n.

4, 6, 15, 65, 77, 133, 91, 319, 209, 341, 299, 481, 493, 799, 527, 1007, 1139, 2449, 703, 3611, 989, 1541, 1643, 3589, 1537, 2407, 2747, 2759, 1829, 3811, 1891, 4633, 2993, 3959, 2627, 4033, 2701, 6157, 3239, 9073, 3569, 5461, 4183, 6439, 5141, 6533

Offset: 0

Patrick De Geest, Oct 13 2001

John Cerkan, Table of n, a(n) for n = 0..10000
John Cerkan, Python 2.7 program

Cf. A001358 (p2 mod p1 = 0), A064899-A064909, A064911, A053409, A046413.

nsp[n_Integer] := nsp[n] = Block[{sp = n + 1}, While[PrimeOmega[sp] != 2, sp++]; sp]; a[n_Integer] := Block[{sp = 4}, While[ fi = FactorInteger@ sp; Mod[fi[[-1, 1]], fi[[1, 1]]] != n, sp = nsp[sp]]; sp]; Array[a, 46, 0] (* Robert G. Wilson v, Aug 20 2025 *)

Name amended by John Cerkan, Apr 12 2018

A049236 a(n) is the number of distinct prime factors of prime(n) + 2.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 2, 3, 2, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2

Offset: 1

Labos Elemer

			prime(27) = 103, prime(27) + 2 = 105 = 3*5*7 has 3 prime factors, so a(27) = 3.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A000040, A001221, A001359, A052147, A064909, A064910, A064911.

Table[Length[FactorInteger[Prime[n] + 2]], {n, 1, 50}] (* G. C. Greubel, May 12 2017 *)

a(n) = omega(prime(n) + 2); \\ Amiram Eldar, Sep 16 2024

a(n) = A001221(A052147(n)). - Amiram Eldar, Sep 16 2024

cp's OEIS Frontend

A064910 Smallest semiprime p*q such that q >= p and q mod p = n.

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