A246445 -id:A246445 - cp's OEIS frontend

A247033 Numbers of the form (3^k - 3)/k.

0, 3, 8, 48, 121, 312, 16104, 122640, 7596480, 61171656, 4093181688, 2366564736720, 19924948267224, 12169835294351280, 889585277491970400, 7633882962663652968, 565719454445904325272, 365721616371321130128240, 239498069351503974657030696, 2084811062715550992506283600

Offset: 1

Juri-Stepan Gerasimov, Sep 09 2014

nonn

Generated by k: 1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 66, 67, ...

Subsequence of A246445.

			121 is in this sequence because (3^k - 3)/k = (3^6 - 3)/6 = 121.

Cf. A000040, A005935, A064535 (with form (2^k - 2)/k), A122780 (nonprimes k in a(n)), A246445, A247307 (with form (4^k - 4)/k).

A247307 Numbers of the form (4^k - 4)/k.

Original entry on oeis.org

0, 6, 20, 63, 204, 682, 2340, 381300, 1398101, 5162220, 71582788, 1010580540, 14467258260, 3059510616420, 2573485501354569, 9938978487990060, 148764065110560900, 510526106256177860940, 117943982401427236556700, 1799331452449680632120820

Offset: 1

Juri-Stepan Gerasimov, Sep 11 2014

nonn

Subsequence of A246445.
Generated by k = 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 15, 17, 19, 23, 28, 29, 31,. ..
This set of k contains all terms of A122781 and all primes. [It contains the primes because j^p == j (mod p) for every integer j if p is prime; see e.g. the corollary 4.4 to the Lagrange theorem in Jones et al.]

			a(9) = 1398101 because (4^12 - 4)/12 = 1398101 for k = 12.

G. A. Jones and J. M. Jones, Congruences with a prime-power modulus, p 65-82 in "Elementary Number Theory", Springer Undergraduate Mathematics Series, (1988).

Cf. A020136, A064535, A122781, A246445, A247033.

lista(nn) = {for (k=1, nn, va = (4^k - 4)/k; if (type(va) == "t_INT", print1(va, ", ")););} \\ Michel Marcus, Sep 12 2014

cp's OEIS Frontend

A247033 Numbers of the form (3^k - 3)/k.

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