A335774 Numbers k such that in prime factorization of k the second smallest factor is 7.

14, 21, 28, 35, 56, 63, 98, 112, 147, 154, 175, 182, 189, 196, 224, 231, 238, 245, 266, 273, 308, 322, 357, 364, 385, 392, 399, 406, 434, 441, 448, 455, 476, 483, 518, 532, 567, 574, 595, 602, 609, 616, 644, 651, 658, 665, 686, 693, 728, 742, 777, 784, 805, 812, 819, 826, 854, 861

Offset

1,1

Comments

Trivially, all terms are multiples of 7. Also terms are divisible by 2 or 3 or 5, and by any number of primes > 7.

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

From Elmo R. Oliveira, Jul 01 2026: (Start)

a(n) = 7 * A374277(n).

a(n) = a(n-1) + a(n-14) - a(n-15).

G.f.: 7*x * (1 + x^2) * (1 + x + x^2) * (2 - x - 2*x^2 + 3*x^3 + 3*x^4 - 5*x^5 + 3*x^6 + 3*x^7 - 2*x^8 - x^9 + 2*x^10) / ((1 - x) * (1 - x^14)). (End)

Example

14 = 2*7, 28 = 2*2*7, 35 = 5*7, 56 = 2^3*7, 63 = 3*3*7, 147 = 3*7*7, 154 = 2*7*11.

Mathematica

Select[Range[14, 1000], 1 < Length[fi = FactorInteger[#]] && 7 == fi[[2, 1]] &]

Crossrefs

Subsequence of A080671.

Cf. A008589 (multiples of 7), A374277.

Sequence in context: A110478 A125967 A284808 * A006625 A389980 A114382

Adjacent sequences: A335771 A335772 A335773 * A335775 A335776 A335777

Keyword

nonn,easy,changed

Author

Zak Seidov, Jun 22 2020

Status

approved