

A219978


Numbers k (>= 1) such that A007781(k1) = k^k  (k1)^(k1) is semiprime.


0



5, 6, 13, 16, 18, 21, 22, 28, 29, 37, 46, 60, 71, 84
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OFFSET

1,1


COMMENTS

This is to A072164 as semiprimes A001358 are to primes A000040. Can thus be called power difference semiprimes.
a(15) >= 115, as 115^115  114^114 is a 237digit composite number with no known factors.  Tyler Busby, Feb 12 2023


LINKS



FORMULA



EXAMPLE

a(1) = 5 because 5^5  4^4 = 2869 = 19 * 151 is semiprime.
a(2) = 6 because 6^6  5^5 = 43531 = 101 * 431.
a(3) = 13 because 13^13  12^12 = 293959006143997 = 28201 * 10423708597.
a(4) = 16 because 16^16  15^15 = 18008850183328692241 = 109 * 165218809021364149.


MATHEMATICA

Flatten[Position[Differences[Table[n^n, {n, 85}]], _?(PrimeOmega[#]==2&)]]+1 (* Harvey P. Dale, Aug 29 2021 *)


PROG

(PARI) isok(n) = bigomega(n^n  (n1)^(n1)) == 2; \\ Michel Marcus, Feb 11 2020


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



