A291972 a(n) is the smallest k such that psi(k)/phi(k) prime where k is the product of n distinct primes.

2, 15, 78, 910, 16770, 399126, 4849845, 27606810, 1543735830, 46091541210, 3546424866270, 84404911817226, 10124919639292458, 388334647332742110, 50538403948689240870, 209239673740280773590, 27738324896530958239530, 3327392973457778860124490

Offset

1,1

Comments

Least k = Product_{i=1..n} p_i such that Product_{i=1..n} (p_i+1)/(p_i-1) is a prime number where p_i is i-th prime divisor of k.

All terms are squarefree. - Charles R Greathouse IV, Sep 07 2017

Links

Table of n, a(n) for n=1..18.

Example

a(3) = 78 = 2*3*13 because psi(78) / phi(78) = 7 is prime and 78 is the least number with this property.

Prog

(PARI) has(f, n)=if(#f~ != n || vecmax(f[, 2])>1, return(0)); my(p=prod(i=1, #f~, 2/(f[i, 1]-1) + 1)); denominator(p)==1 && isprime(p)
a(n)=my(mn=prod(i=1, n, prime(i)), mx=2*mn); while(1, forfactored(k=mn, mx, if(has(k[2], n), return(k[1]))); mn=mx; mx*=2) \\ Charles R Greathouse IV, Sep 07 2017

Crossrefs

Cf. A000010, A001615.

Sequence in context: A102289 A041243 A216247 * A056079 A266622 A036239

Adjacent sequences: A291969 A291970 A291971 * A291973 A291974 A291975

Keyword

nonn

Author

Altug Alkan, Sep 07 2017

Extensions

a(10)-a(18) from Charles R Greathouse IV, Sep 07 2017

Status

approved