OFFSET
1,2
COMMENTS
Sigma preserves both the 2-adic and 3-adic valuation of the terms of this sequence.
All 65 known 5-multiperfect numbers (A046060) are included in this sequence, as well as the smallest 7-multiperfect number, 141310897947438348259849402738485523264343544818565120000 = A007539(7), and probably the majority of other p-multiperfect numbers as well, where p is a prime > 3. However, any term that is in A349747 is not included in this sequence.
LINKS
FORMULA
MATHEMATICA
f[p_, e_] := NextPrime[p, 2]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := n * GCD[(sigma = DivisorSigma[1, n]), (u = s[n])] == sigma * GCD[n, u]; Select[Range[10^6], q] (* Amiram Eldar, Dec 01 2021 *)
PROG
(PARI)
A003961twice(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(1+nextprime(1+f[i, 1]))); factorback(f); };
isA349746(n) = { my(s=sigma(n), u=A003961twice(n)); (n*gcd(s, u) == (s*gcd(n, u))); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 30 2021
EXTENSIONS
a(15)-a(25) from Martin Ehrenstein, Dec 17 2021
STATUS
approved