A054905 Smallest composite x such that sigma(x) + 2n = sigma(x + 2n).

434, 305635357, 104, 27, 195556, 65, 12, 39, 20, 56, 916, 80, 212282, 57, 44, 106645, 52, 125

Offset

1,1

Comments

a(19) > 4293000000, if it exists. - Jud McCranie, May 25 2000

a(19) > 10^11, if it exists. - Charles R Greathouse IV, Oct 26 2022

Links

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

Mauro Fiorentini, Le soluzioni dell’equazione s(n + k) = s(n) + k, con n composto fino a 109 e k sino a 1000.

Example

a(5) corresponds to n=3+2=5, d=2n=10 and the smallest composite integer is 195556. The next solution is 1152136225.

Prog

(PARI) a(n)=forcomposite(x=3, 10^66, if(sigma(x)+2*n==sigma(x+2*n), return(x)));
for(n=1, 66, print1(a(n), ", ")); \\ Joerg Arndt, Nov 15 2014
(PARI) a19(lim, startAt=39)=startAt=ceil(startAt); my(v=vectorsmall(38), i=(startAt-1)%38); forfactored(n=startAt, lim\1+38, my(t=sigma(n)); if(i++>38, i=1); if(t==v[i]+38, return(n[1]-38)); v[i]=if(vecsum(n[2][, 2])>1, t, 0)) \\ Charles R Greathouse IV, Oct 25 2022

Crossrefs

Cf. A015913, A015914, A015915, A015916, A015917, A054799.

Cf. A023200, A023201, A023202, A023203,

Sequence in context: A050507 A145318 A054987 * A160353 A268475 A212227

Adjacent sequences: A054902 A054903 A054904 * A054906 A054907 A054908

Keyword

nonn,more

Author

Labos Elemer May 23 2000

Extensions

Description corrected by Jud McCranie, May 25 2000

Status

approved