A337044 Numbers k such that both k and sigma(k)=A000203(k) are powerful, i.e., are terms of A001694.

1, 81, 343, 400, 9261, 27783, 32400, 137200, 189728, 224939, 972000, 1705636, 2205472, 3087000, 3591200, 3648100, 3704400, 7968032, 11113200, 13645088, 15350724, 15367968, 18220059, 21161304, 24240600, 25992000, 26680500, 29184800, 32832900, 48586824, 51595489

Offset: 1

Author

Andrew Howroyd and Hugo Pfoertner, Aug 12 2020

Keywords

• nonn

Comments

From David A. Corneth, Aug 14 2020: (Start)

If coprime numbers k and m are in the sequence then k*m is in the sequence.

Up to 10^15, the largest prime divisor of a term is 178987 for which the product of the primes with multiplicity 1 of sigma(178987^2) is 16653 = 3 * 7 * 13 * 61. The second largest prime divisor is 25073 (for which sigma(25073^2) has a product of primes with multiplicity 1 of 341 = 11 * 31), which is quite a bit smaller than 178987. Can we somehow constrain the list of possible prime divisors to ease computation? (End)

Links

• David A. Corneth, Table of n, a(n) for n = 1..10324 (terms <= 10^18)
• David A. Corneth, PARI program

Crossrefs

Cf. A000203, A001694, A180090, A337045.

Programs

PARI

for(k=1, 60000000, if(ispowerful(k) && ispowerful(sigma(k)), print1(k, ", ")))

PARI

\\ See Corneth link \\ David A. Corneth, Aug 14 2020