A357917 - OEIS

A357917

a(n) is the least k such that phi(k) + d(k) = A357916(n), where phi(k) = A000010(k) is Euler's totient function, and d(k) = A000005(k) is the number of divisors of k.

1, 2, 4, 16, 25, 81, 121, 256, 484, 1296, 529, 1024, 1600, 2116, 2401, 7744, 11664, 5041, 7225, 11236, 20164, 10201, 25600, 12769, 30976, 46656, 21025, 17161, 44944, 51076, 29929, 84100, 73984, 36481, 75076, 107584, 54289, 63001, 87025, 69169, 101761, 126025, 215296, 256036, 252004, 295936

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers k such that A061468(k) = phi(k) + d(k) is prime, and no smaller number gives the same value of A061468, sorted in order of the prime values.

All terms except 2 are squares, because if k > 2, phi(k) is even, and if d(k) is odd, k must be a square.

All numbers in this sequence are elements of A225983. For an example, this excludes all numbers of the form (6*m)^2 but only if m is not divisible by 6. - Thomas Scheuerle, Oct 20 2022

LINKS

Robert Israel, Table of n, a(n) for n = 1..3000

FORMULA

A061468(a(n)) = A000010(a(n)) + A000005(a(n)) = A357916(n).

EXAMPLE

a(4) = 16 because phi(16) + d(16) = 8 + 5 = 13 = A357916(4), and no smaller number than 16 works.

MAPLE

N:= 10^6:

pmax:= evalf(N/(exp(gamma)*log(log(N))+3/log(log(N))));

V:= 'V': P:= {3}: V[3]:= 2:

for k from 1 to sqrt(N) do

n:= k^2;