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A349176
Odd numbers k for which gcd(k, A003961(k)) = gcd(sigma(k), A003961(k)) > 1, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
4
135, 285, 435, 455, 855, 885, 1185, 1287, 1305, 1335, 1425, 1435, 1485, 1635, 2235, 2275, 2295, 2655, 2685, 2905, 2985, 3105, 3135, 3185, 3311, 3395, 3435, 3555, 3585, 4005, 4035, 4185, 4425, 4785, 4865, 4905, 4995, 5385, 5685, 5805, 5835, 5845, 5925, 6135, 6237, 6335, 6345, 6585, 6675, 6735, 7125, 7155, 7175, 7185
OFFSET
1,1
EXAMPLE
For n = 135 = 3^3 * 5, sigma(135) = 240 = 2^4 * 3 * 5, A003961(135) = 5^3 * 7 = 875, and gcd(135,875) = gcd(240,875) = 5, which is larger than 1, therefore 135 is included in the sequence.
MATHEMATICA
Select[Range[1, 7200, 2], And[#1/#2 == #1/#3, #2 > 1] & @@ {#3, GCD[#1, #3], GCD[#2, #3]} & @@ {#, DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &] (* Michael De Vlieger, Nov 11 2021 *)
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA349176(n) = if(!(n%2), 0, my(u=A003961(n), t=gcd(u, n)); (t>1)&&(gcd(u, sigma(n))==t));
CROSSREFS
Intersection of A104210 and A349174, or equally, intersection of A349166 and A349174.
Subsequence of A372567.
Sequence in context: A274434 A325569 A372567 * A342189 A374461 A176313
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 11 2021
STATUS
approved