OFFSET
1,2
COMMENTS
In other words, numbers m such that if p^k is the greatest power of any prime p which divides m, then k is a term > 1 in A001694.
Subsequence of A001694 (since all prime exponents are > 1).
Compare with A361177, of which this is a subsequence (see Formula).
Distinct from A277562; A277652(26) = 331776 = 2^12 * 3^4 is not in this sequence. - Michael De Vlieger, Apr 30 2024
1 and 41472 are two terms here that are not in A277562. - David A. Corneth, Apr 30 2024
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1580 terms from Michael De Vlieger)
FORMULA
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=2} 1/p^A001694(k)) = 1.08410926642148594327... . - Amiram Eldar, May 12 2024
EXAMPLE
MATHEMATICA
nn = 2^21; f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]]; Select[Union@ Flatten@ Table[a^7*b^6*c^5*d^4, {d, Surd[nn, 4]}, {c, Surd[nn/d^4, 5]}, {b, Surd[nn/(c^5*d^4), 6]}, {a, Surd[nn/(b^6*c^5*d^4), 7]}], AllTrue[FactorInteger[#][[All, -1]], Divisible[#, f[#]^2] &] &] (* Michael De Vlieger, Apr 29 2024 *)
PROG
(PARI) isok(k) = if (ispowerful(k), my(f=factor(k)[, 2]); #select(ispowerful, f) == #f); \\ Michel Marcus, Apr 30 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
David James Sycamore, Apr 29 2024
EXTENSIONS
More terms from Michael De Vlieger, Apr 29 2024
STATUS
approved