A350516 a(n) is the least k>1 such that omega(k) is equal to (omega(n*k + 1) - 1)/n.

5, 97, 443, 5801, 42697, 7813639, 10303967, 1225192093

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 09 2022

Keywords

• nonn
• more

Comments

Are all terms prime numbers?

a(9) <= 14567138141, a(10) <= 5509396663871, a(11) <= 4128894057139, a(12) <= 13264466350165447, a(13) <= 6115610326638653. - Daniel Suteu, Mar 14 2022

Examples

			a(2) = 97 because omega(97) = (omega(2*97 + 1) - 1)/2 = (omega(3*5*13) - 1)/2 = 1.
		

Crossrefs

Cf. A001221 (omega).

Programs

Mathematica

a[n_] := Module[{k = 2}, While[PrimeNu[k] != (PrimeNu[n*k + 1] - 1)/n, k++]; k]; Array[a, 5] (* Amiram Eldar, Mar 09 2022 *)

PARI

a(n) = my(k=2); while (omega(k) != (omega(n*k + 1) - 1)/n, k++); k; \\ Michel Marcus, Mar 09 2022

Python

from sympy import factorint
for n in range(1, 8):
    for k in range(2, 10**10):
        if len(factorint(k).keys())*n+1==len(factorint(k*n+1).keys()):
            print(n, k)
            break # Martin Ehrenstein, Mar 14 2022

Extensions

a(8) from Martin Ehrenstein, Mar 14 2022