A371085 -id:A371085 - cp's OEIS frontend

A371083 Nonsquarefree numbers that are not divisible by p^p for any prime p.

9, 18, 25, 45, 49, 50, 63, 75, 90, 98, 99, 117, 121, 125, 126, 147, 150, 153, 169, 171, 175, 198, 207, 225, 234, 242, 245, 250, 261, 275, 279, 289, 294, 306, 315, 325, 333, 338, 342, 343, 350, 361, 363, 369, 375, 387, 414, 423, 425, 441, 450, 475, 477, 490, 495, 507, 522, 525, 529, 531, 539, 549, 550, 558, 575, 578

Offset: 1

Antti Karttunen, Mar 12 2024

nonn

The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^p) - 6/Pi^2 = 0.1140631325... . - Amiram Eldar, Mar 12 2024

Antti Karttunen, Table of n, a(n) for n = 1..10000

Intersection of A013929 and A048103.

Cf. A371084 (characteristic function), A371085 (subsequence), A059956.

PARI
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\\ See A371083.
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A371086 Nonsquarefree numbers k such that A003557(k) divides A276086(k), where A003557(k) is k divided by its largest squarefree divisor, and A276086 is the primorial base exp-function.

Original entry on oeis.org

9, 25, 45, 49, 50, 63, 75, 98, 99, 117, 147, 153, 171, 175, 207, 225, 242, 245, 261, 279, 294, 315, 325, 333, 343, 350, 363, 369, 375, 387, 423, 475, 477, 490, 495, 525, 531, 539, 549, 550, 585, 603, 605, 625, 639, 650, 657, 693, 711, 726, 735, 747, 765, 775, 801, 819, 825, 833, 847, 850, 855, 873, 909, 925, 927, 931

Offset: 1

Antti Karttunen, Mar 12 2024

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to primorial base

Intersection of A013929 and A371088.

Cf. A003557, A276086, A371085 (subsequence).

A003557(n) = (n/factorback(factor(n)[, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA371086(n) = (!issquarefree(n) && !(A276086(n)%A003557(n)));

cp's OEIS Frontend

A371083 Nonsquarefree numbers that are not divisible by p^p for any prime p.

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