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A164977 Numbers m such that the set {1..m} has only one nontrivial decomposition into subsets with equal element sum. 9
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} }.

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, 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 March 25 20:10 EDT 2019. Contains 321477 sequences. (Running on oeis4.)