A282175 a(n) is the smallest product M=p_1*p_2*...*p_n with distinct primes p_i such that M+2^n=B, where B=q_1*q_2*...*q_n with distinct primes q_i, or a(n)=0 if there is no such M.

3, 6, 70, 2030, 42978, 1788710, 63905142, 5705962314, 888081948858, 120056591419170

Offset

1,1

Comments

Conjecturally all a(n)>0.

Since d(a(n)+2^n) = 2^n, where d(n) is the number of divisors of n, and d(a(n)+d(a(n)+2^n)) = d(a(n)), then it is a subsequence of sequence A175304.

Links

Table of n, a(n) for n=1..10.

Example

For n=3,...,8, we have the following numbers M, B=M+2^n and their prime divisors:
70 = 2 5 7; 78 = 2 3 13.
2030 = 2 5 7 29; 2046 = 2 3 11 31.
42978 = 2 3 13 19 29; 43010 = 2 5 11 17 23.
1788710 = 2 5 7 11 23 101; 1788774 = 2 3 13 17 19 71.
63905142 = 2 3 7 17 37 41 59; 63905270 = 2 5 11 13 23 29 67.
5705962314 = 2 3 13 17 19 23 43 229; 5705962570 = 2 5 7 11 29 59 61 71.

Crossrefs

Sequence in context: A296374 A362822 A205081 * A182966 A023174 A350992

Adjacent sequences: A282172 A282173 A282174 * A282176 A282177 A282178

Keyword

nonn,more

Author

Vladimir Shevelev and Peter J. C. Moses, Feb 07 2017

Extensions

a(9)-a(10) from Giovanni Resta, Feb 28 2017

Status

approved