A318988 Totients whose inverses contain two or more consecutive tetrahedral pyramidal numbers.

24, 80, 256, 880, 3840, 8096, 96768, 380160, 552960, 2336256, 6209280, 7600320, 7741440, 10579968, 25090560, 32845824, 34031616, 34594560, 35610624

Offset

1,1

Comments

For a(1) = A000010(A000292(5)) = A000010(A000292(6)) = A000010(A000292(7)), this reduces to A000010(5*7) = A000010(8*7) = A000010(12*7). The number 7 is relatively prime to 5, 8, and 12 which are inverses of the totient value 4. 7 appears in the numerator of A000292(5), A000292(6), and A000292(7). Following the same process 11 and 17 replace 7 for a(2) and a(3).

Conjecture: There are at most three consecutive tetrahedral pyramidal numbers in the set of inverses of a totient number.

Links

Table of n, a(n) for n=1..19.

Example

24 is a term because A000010(A000292(5)) = A000010(A000292(6)) = A000010(A000292(7)) = 24.
80 is a term because A000010(A000292(9)) = A000010(A000292(10)) = 80.
380160 is a term because A000010(A000292(182)) = A000010(A000292(183)) = A000010(A000292(184)) = 380160.

Crossrefs

Cf. A000010, A000292.

Sequence in context: A211583 A211589 A211597 * A182915 A030622 A063456

Adjacent sequences: A318985 A318986 A318987 * A318989 A318990 A318991

Keyword

nonn

Author

Torlach Rush, Sep 06 2018

Status

approved