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A337044 Numbers k such that both k and sigma(k)=A000203(k) are powerful, i.e., are terms of A001694. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

PROG

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

(PARI) \\ See Corneth link \\ David A. Corneth, Aug 14 2020

CROSSREFS

Cf. A000203, A001694, A180090, A337045.

Sequence in context: A237958 A238039 A232284 * A337045 A128607 A180090

Adjacent sequences:  A337041 A337042 A337043 * A337045 A337046 A337047

KEYWORD

nonn

AUTHOR

Andrew Howroyd and Hugo Pfoertner, Aug 12 2020

STATUS

approved

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)