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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A337183 A112417 A139693 * A266552 A263716 A175899

Adjacent sequences:  A182073 A182074 A182075 * A182077 A182078 A182079

KEYWORD

nonn,easy

AUTHOR

Michel Lagneau, Apr 10 2012

STATUS

approved

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Last modified April 15 23:04 EDT 2021. Contains 343007 sequences. (Running on oeis4.)