OFFSET

1,3

COMMENTS

In the first 250000 terms the smallest numbers that have not appeared are 64, 1024, 11664, 15625. It is unknown if these and all other numbers eventually appear.

See A355637 for the fixed points.

LINKS

Scott R. Shannon, Image of the first 250000 terms. The green line is y = n.

EXAMPLE

a(6) = 6 as a(4) + a(5) = 9 + 18 = 27 which has four divisors, and 6 is the smallest unused number that does not equal 27 and has four divisors.

PROG

(PARI) listm(nn) = my(va = vector(nn)); va[1] = 1; va[2] = 1; my(m = Map()); mapput(m, 1, 1); for (n=3, nn, my(s=va[n-2]+va[n-1], d=numdiv(s), k=1, vs=Vec(va, n-1)); while (mapisdefined(m, k) || (k==s) || (numdiv(k)!=d), k++); va[n] = k; mapput(m, k, n); ); va; \\ Michel Marcus, Jul 11 2022

(Python)

from sympy import divisor_count

from itertools import count, islice

def agen():

anm1, an, mink, seen = 1, 1, 2, {1}

yield 1

for n in count(2):

yield an

k, target, tsum = mink, divisor_count(anm1+an), anm1+an

while k in seen or k == tsum or divisor_count(k) != target: k += 1

while mink in seen: mink += 1

anm1, an = an, k

seen.add(an)

print(list(islice(agen(), 73))) # Michael S. Branicky, Jul 26 2022

CROSSREFS

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Jul 11 2022

STATUS

approved