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A164977 Numbers m such that the set {1..m} has only one nontrivial decomposition into subsets with equal element sum. 10
3, 4, 5, 6, 10, 13, 22, 37, 46, 58, 61, 73, 82, 106, 157, 166, 178, 193, 226, 262, 277, 313, 346, 358, 382, 397, 421, 457, 466, 478, 502, 541, 562, 586, 613, 661, 673, 718, 733, 757, 838, 862, 877, 886, 982, 997, 1018, 1093, 1153, 1186, 1201, 1213, 1237, 1282 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers m such that m*(m+1)/2 has exactly two divisors >= m.

Also numbers m such that m*(m+1)/2 is the product of two primes.

LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

FORMULA

{ m :  A035470(m) = 2 }.

{ m :  A164978(m) = 2 }.

{ m : |{d|m*(m+1)/2 : d>=m}| = 2 }.

{ m :  m*(m+1)/2 in {A068443} }.

{ m :  m*(m+1)/2 in {A001358} }.

{ m :  A069904(m) = 2 }.

EXAMPLE

10 is in the sequence, because there is only one nontrivial decomposition of {1..10} into subsets with equal element sum: {1,10}, {2,9}, {3,8}, {4,7}, {5,6}; 11|55.

13 is in the sequence with decomposition of {1..13}: {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, {6,7}, {13}; 13|91.

MAPLE

a:= proc(n) option remember; local k;

      for k from 1+ `if`(n=1, 2, a(n-1))

      while not (isprime(k) and isprime((k+1)/2)

              or isprime(k+1) and isprime(k/2))

      do od; k

    end:

seq(a(n), n=1..100);

MATHEMATICA

Select[Range@1304, PrimeOmega[#] + PrimeOmega[# + 1] == 3 &] (* Robert G. Wilson v, Jun 28 2010 and updated Sep 21 2018 *)

PROG

(PARI) is(n)=if(isprime(n), bigomega(n+1)==2, isprime(n+1) && bigomega(n)==2) \\ Charles R Greathouse IV, Sep 08 2015

CROSSREFS

Cf. A164978, A035470, A068443, A069904, A001358.

Sequence in context: A219041 A218946 A174057 * A103033 A099561 A110300

Adjacent sequences:  A164974 A164975 A164976 * A164978 A164979 A164980

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 03 2009

STATUS

approved

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Last modified August 24 16:16 EDT 2019. Contains 326295 sequences. (Running on oeis4.)