A353562 Prime shadows of highly composite numbers, A002182.

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

Author

Antti Karttunen, Apr 29 2022

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Cf. also A353561, A353568.

Programs

PARI

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));

Formula

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

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