A307137 Terms of A194269 that are not squares of primes.

68, 17500, 5053176, 435034872, 3079148398, 107924794257, 122918945808

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 can be thought of as the set of integers that satisfy Sum_{i=1..k} d(i)^i = j+1 for k > 2.

Also in the sequence are 63602175290616, 27232626132792608, 131685306017557752 and 1125089196456707568267636780. - Daniel Suteu, Mar 28 2019

a(8) > 2.5*10^11. 146891545244361186001164385301664828062299990188246080274986418 and 1074195891803336036687617104130500495489848428998310547357799403665 are also terms. - Giovanni Resta, Mar 29 2019

Links

Table of n, a(n) for n=1..7.

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); ); } \\ A194269
isok2(n) = issquare(n) && isprime(sqrtint(n));
isok(n) = isok1(n) && !isok2(n);

Crossrefs

Cf. A001248, A194269.

Sequence in context: A267064 A159365 A145623 * A230685 A093234 A177666

Adjacent sequences: A307134 A307135 A307136 * A307138 A307139 A307140

Keyword

nonn,more

Author

Michel Marcus, Mar 26 2019

Extensions

a(6)-a(7) from Giovanni Resta, Mar 29 2019

Status

approved