A378983 Numbers k such that (A003961(k)-2*k) divides (A003961(k)-(1+sigma(k))), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

1, 2, 3, 4, 5, 8, 10, 11, 15, 16, 17, 25, 26, 29, 32, 33, 35, 39, 41, 57, 59, 64, 71, 93, 101, 107, 125, 128, 137, 149, 161, 179, 191, 197, 227, 239, 256, 269, 281, 311, 347, 419, 431, 461, 512, 521, 569, 599, 617, 641, 659, 782, 809, 821, 827, 857, 881, 1019, 1024, 1030, 1031, 1034, 1049, 1054, 1061, 1091, 1151

Offset: 1

Author

Antti Karttunen, Dec 13 2024

Keywords

• nonn

Comments

Conjecture: A202274 gives all terms of A028982 that occur in this sequence.

Examples

			For k=16 we have A003961(16) = 81, A003961(k)-2*k = 49, and 49 divides (A003961(k)-(1+sigma(k))) = 81-32 = 49, therefore 16 is included in this sequence.
For k=25 we have A003961(25) = 49, A003961(k)-2*k = -1, and -1 divides (A003961(k)-(1+sigma(k))) regardless of what the latter is, therefore 25 is included.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Positions of 0's in A378982.

Subsequences: A048674, A348514, A202274.

Cf. also A378980.

Programs

PARI

isA378983(n) = !A378982(n);