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

1,2

Comments

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

Links

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

Example

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.

Prog

(PARI) isA378983(n) = !A378982(n);

Crossrefs

Positions of 0's in A378982.

Subsequences: A048674, A348514, A202274.

Cf. also A378980.

Sequence in context: A047597 A309960 A247935 * A005233 A155736 A074897

Adjacent sequences: A378980 A378981 A378982 * A378984 A378985 A378986

Keyword

nonn

Author

Antti Karttunen, Dec 13 2024

Status

approved