A182076 Smallest number k such that the difference between the greatest prime divisor of k and the product of the other distinct prime divisors equals n.

2, 3, 10, 5, 14, 7, 78, 33, 22, 11, 26, 13, 114, 51, 34, 17, 38, 19, 290, 69, 46, 23, 174, 145, 186, 87, 58, 29, 62, 31, 222, 185, 430, 111, 74, 37, 258, 123, 82, 41, 86, 43, 530, 141, 94, 47, 318, 265, 590, 159, 106, 53, 354, 295, 366, 177, 118, 59, 122, 61

Offset

1,1

Comments

a(n) = n+1 if n+1 is prime.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(7) = 78 because the distinct prime divisors of 78 are {2, 3, 13} and 13 - 2*3 = 7.

Maple

with(numtheory):for n from 1 to 60 do:ii:=0:for k from 2 to 200000 while(ii=0) do:x:=factorset(k):m:=nops(x): s:=product ('x[i] ', 'i'=1..m-1):if s+n = x[m]  then printf(`%d, `, k):ii:=1:else fi:od: od:

Prog

(PARI) a(n)=my(t); for(k=n+1, 4<<n, if(issquarefree(k), t=factor(k)[, 1]; if(t[#t]-k/t[#t]==n, return(k)))) \\ Charles R Greathouse IV, Apr 11 2012
(PARI) a(n)=my(p=nextprime(n+1)); while(!issquarefree(p-n), p=nextprime(p+1)); p*(p-n) \\ Charles R Greathouse IV, Apr 11 2012

Crossrefs

Cf. A001221, A182011.

Sequence in context: A348058 A112417 A139693 * A347271 A266552 A263716

Adjacent sequences: A182073 A182074 A182075 * A182077 A182078 A182079

Keyword

nonn,easy

Author

Michel Lagneau, Apr 10 2012

Status

approved