A351549 Numbers k for which k * gcd(sigma(k), A019565(k)) is equal to sigma(k) * gcd(k, A019565(k)).
1, 1456, 15480, 114660, 2244600, 3894768, 25108200, 27052704, 65021040, 112402080, 1973921400
Offset: 1
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Table[GCD[DivisorSigma[1, n], Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 99}] (* Michael De Vlieger, Feb 20 2022 *)
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); }; A351557(n) = gcd(sigma(n), A019565(n));
Table[If[# == 1, 0, Total[#2*2^PrimePi[#1] & @@@ FactorInteger[#]]/2] &@ GCD[n, Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 102}] (* Michael De Vlieger, Feb 20 2022 *)
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); }; A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; A351558(n) = A048675(gcd(n, A019565(n)));
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