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A255576 Integers n such that Sum_{i=1..t-1} d(i)/d(i+1) is prime, where d(1), ..., d(t) are the divisors of n in ascending order. 1
16, 64, 729, 1024, 1536, 6250, 9375, 16384, 19683, 39366, 1179648, 4194304, 6770688, 9765625, 14348907, 29229255, 39062500, 67108864, 125000000, 335544320 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A227993.

The corresponding primes are 2, 3, 2, 5, 13, 5, 5, 7, 3, 11, 41, 11, 89, 2, 5, 37, 19, 13, 53, 37, ...

a(n) is a power of 2 for n = 1, 2, 4, 8, 12, 18, ... with the corresponding primes 2, 3, 5, 7, 11, 13, ...

a(n) is a perfect square for n = 1, 2, 3, 4, 8, 12, 14, 17, 18, ... with the corresponding primes 2, 3, 2, 5, 7, 11, 2, 19, 13, ...

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

64 is in the sequence because the divisors of 64 are {1, 2, 4, 8, 16, 32, 64} and 1/2 + 2/4 + 4/8 + 8/16 + 16/32 + 32/64 = 3 is prime.

MATHEMATICA

Do[s=0; Do[s=s+Divisors[n][[i]]/Divisors[n][[i+1]], {i, 1, Length[Divisors[n]]-1}]; If[PrimeQ[s]&&!PrimeQ[n], Print[n]], {n, 10^6}]

CROSSREFS

Cf. A227993.

Sequence in context: A175209 A141840 A203281 * A065404 A327496 A330824

Adjacent sequences:  A255573 A255574 A255575 * A255577 A255578 A255579

KEYWORD

nonn,more

AUTHOR

Michel Lagneau, Feb 25 2015

STATUS

approved

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Last modified April 9 17:48 EDT 2020. Contains 333361 sequences. (Running on oeis4.)