

A337455


Numbers of the form m + bigomega(m) with m a positive integer.


0



1, 3, 4, 6, 8, 11, 12, 14, 15, 16, 17, 18, 20, 21, 23, 24, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 44, 45, 47, 48, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 84, 85, 87, 88, 89, 90, 92, 93
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OFFSET

1,2


COMMENTS

If a(n) = m + A001222(m) then (a(n)  m) <= log(a(n))/log(2).
It appears that a(n)/n may converge to a constant around ~ 1.49.


LINKS

Table of n, a(n) for n=1..66.


EXAMPLE

a(7) = 10 + A001222(10) = 10 + 2 = 12


MATHEMATICA

m = 100; Select[Union @ Table[n + PrimeOmega[n], {n, 1, m}], # <= m &] (* Amiram Eldar, Aug 28 2020 *)


PROG

(PARI) upto(limit)={Set(select(t>t<=limit, apply(m>m+bigomega(m), [1..limit])))} \\ Andrew Howroyd, Aug 27 2020


CROSSREFS

Cf. A001222 (bigomega), A064800.
Numbers of the form k^n+n where k is prime are subsequences: A006127 (k=2), A104743 (k=3), A104745 (k=5), A226199 (k=7), A226737 (k=11).
A008864, A101340, and A160649 (excluding the first term) are subsequences.
Sequence in context: A176986 A325455 A069357 * A080728 A047414 A109402
Adjacent sequences: A337452 A337453 A337454 * A337456 A337457 A337458


KEYWORD

nonn


AUTHOR

Nathan J. McDougall, Aug 27 2020


STATUS

approved



