OFFSET
1,1
COMMENTS
A194269 lists the integers j that satisfy Sum_{i=1..k} d(i)^i = j+1 for some k where d() is the sorted list of divisors of j.
All squares of primes (A001248) are in A194269 (with k=2), but some terms of A194269 are not in A001248.
So the sequence consists of the integers that satisfy Sum_{i=1..k} d(i)^i = j+1 for k > 2.
a(1) = 68 = 1 + 2^2 + 4^3 is the only term with k = 3; the others should have k > 3. - Max Alekseyev, Nov 18 2024
Also in the sequence is 1125089196456707568267636780. - Daniel Suteu, Mar 28 2019
146891545244361186001164385301664828062299990188246080274986418 and 1074195891803336036687617104130500495489848428998310547357799403665 are also terms. - Giovanni Resta, Mar 29 2019
No other terms below 10^22. Also contains 1397818536728878029228901636216061803887128332853093401018283627886158780 and 187-digit number Sum_{i=1..52} A027750(734441344,i)^i. - Max Alekseyev, Nov 22 2024
EXAMPLE
The divisors of 68 are 1, 2, 4, 17, 34, 68; 1^1 + 2^2 + 4^3 = 69, so 68 is a term.
PROG
(PARI) isok1(n) = {my(d=divisors(n), s=0); for(k=1, #d, s += d[k]^k; if (s == n+1, return (k)); if (s > n+1, break); ); 0; } \\ A194269
isok(n) = isok1(n) && isprimepower(n)!=2;
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michel Marcus, Mar 26 2019
EXTENSIONS
a(6)-a(7) from Giovanni Resta, Mar 29 2019
a(8)-a(10) from Daniel Suteu confirmed by Max Alekseyev, Nov 18 2024
STATUS
approved