A353561 -id:A353561 - cp's OEIS frontend

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

Antti Karttunen, Apr 29 2022

nonn

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.

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

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

Cf. also A353561, A353562.

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));

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

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

A353562 Prime shadows of highly composite numbers, A002182.

Original entry on oeis.org

1, 2, 3, 4, 6, 10, 9, 14, 12, 20, 18, 28, 30, 42, 40, 36, 56, 60, 84, 100, 132, 140, 156, 126, 120, 196, 198, 168, 200, 264, 280, 312, 252, 440, 392, 396, 520, 336, 400, 528, 560, 624, 504, 880, 784, 792, 1040, 840, 936, 1360, 1320, 1176, 1120, 1560, 1008, 1760, 1568, 1584, 2080, 1680, 1872, 2720, 2640, 2352, 2240, 3120

Offset: 1

Antti Karttunen, Apr 29 2022

nonn

Sequence is injective (no duplicate values occur) because A002182 is a subsequence of A025487.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002182, A025487, A122111, A181819, A329902.

Cf. also A353561, A353568.

v002182 = readvec("b002182_to.txt"); \\ Prepared from b-file of A002182 with gawk ' { print $2 } '
A002182(n) = v002182[n];
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A353562(n) = A181819(A002182(n));

a(n) = A181819(A002182(n)).

a(n) = A122111(A329902(n)).

cp's OEIS Frontend

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

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