A291487 a(n) is the smallest k such that psi(k) = n!, or 0 if no such k exists (psi(k) = A001615(k)).

1, 1, 0, 4, 12, 75, 300, 1950, 13650, 122850, 1160250, 13340250, 140390250, 1825073250, 25318743450, 370489869750, 5503458610650, 93558796381050, 1643961707838450, 30815473745606550, 596477734382780250, 12526032422038385250, 272871020017346000250, 6276033460398958005750

Offset: 0

Author

Altug Alkan, Aug 24 2017

Keywords

• nonn

Examples

			a(5) = 75 because psi(75) = 120 = 5! and 75 is the least number with this property.
a(7) = 1950 and 1950 has no prime factor 7, so a(8) = 7*1950 = 13650.
		

Crossrefs

Cf. A000142, A001615.

Programs

PARI

a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))
a(n) = my(N=n!); for(k=1, N, if(a001615(k)==N, return(k))); 0 \\ after Charles R Greathouse IV at A001615

Extensions

a(13)-a(14) from Giovanni Resta, Aug 25 2017

a(15)-a(23) from Daniel Suteu, Dec 29 2020