A291356 a(n) is the smallest k such that usigma(k) = A002110(n), or 0 if no such k exists.

1, 0, 5, 18, 164, 1538, 20018, 408404, 7759748, 148728578, 0, 194482899488, 0, 286353189202064, 0, 491911826070793124, 32087786808310197824, 1809656800145141307344, 113734187984879487014048, 0, 0, 27153120399499349433747548978, 0

Offset: 0

Author

Amiram Eldar and Altug Alkan, Aug 23 2017

Keywords

• nonn
• more

Examples

			a(3) = 18 because usigma(18) = 30 = A002110(3) and 18 is the smallest number with this property.
		

Crossrefs

Cf. A002110, A034448, A289126.

Programs

PARI

nthprimorial(n)=prod(i=1,n, prime(i));
usigma(n,f=factor(n))=prod(i=1,#f~, f[i,1]^f[i,2]+1);
a(n)=my(target=nthprimorial(n)); forfactored(n=target*nthprimorial(n-1)\usigma(nthprimorial(n-1)),target, if(usigma(n[1],n[2])==target, return(n[1]))); 0 \\ Charles R Greathouse IV, Aug 23 2017

Extensions

a(10)-a(18) from Giovanni Resta, Aug 23 2017

a(19)-a(22) from Daniel Suteu, Dec 29 2020