A353568 Prime shadows of (nonzero) K-champion numbers.

1, 3, 4, 5, 6, 10, 9, 14, 15, 22, 20, 21, 26, 28, 33, 30, 35, 44, 39, 42, 55, 52, 51, 66, 65, 68, 70, 57, 78, 85, 110, 102, 95, 130, 114, 170, 138, 182, 220, 190, 174, 238, 260, 230, 255, 266, 340, 290, 276, 285, 322, 380, 310, 418, 345, 476, 406, 460, 370, 510, 506, 435, 532, 434, 580, 483, 570, 638, 465, 644, 518

Offset: 1

Author

Antti Karttunen, Apr 29 2022

Keywords

• nonn

Comments

Sequence is injective (no duplicate values occur) because A307866 (after its initial zero) is a subsequence of A025487.

The finite number of powerful (A001694) terms in A307866 implies a finite number of odd terms in this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..883

Crossrefs

Cf. A025487, A122111, A181819, A307866, A330686.

Cf. also A353561, A353562.

Programs

PARI

v307866 = readvec("b307866_to.txt";) \\ Prepared from the b-file of A307866 with gawk ' { print $2 } ' < b307866.txt > b307866_to.txt
A307866(n) = v307866[n];
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A353568(n) = A181819(A307866(1+n));

Formula

a(n) = A181819(A307866(1+n)).

a(n) = A122111(A330686(n)).