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A181177 Numbers k such that k^2 + 1 = p*q, p and q primes gives the sums p+q not unique. 2
22, 34, 46, 50, 28, 44, 76, 80, 100, 42, 114, 104, 136, 86, 254, 266, 274, 58, 106, 154, 194, 286, 334, 324, 456, 504, 516, 214, 374, 494, 526, 566, 140, 520, 78, 186, 354, 426, 530, 670, 366, 546, 726, 166, 614, 92, 220, 316, 620, 836, 844, 390, 414, 810 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We obtain the subsets of numbers with the same sum of prime divisors:

(22, 34, 46, 50), (28, 44, 76), (80, 100),... => sums 102, 162, 210, ...

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

22^2 + 1 = 5*97 and 97 + 5 = 102 ;

34^2 + 1 = 13*89 and 13 + 89 = 102 ;

46^2 + 1 = 29*73 and 29 + 73 = 102 ;

50^2 + 1 = 41*61 and 41 + 61 = 102.

MAPLE

# storage of sums and indices

with(numtheory): nn:=350: T:=array(1..nn): U:=array(1..1000): B:=array(1..nn): V:=array(1..1000): k:=1: for p from 1 to 1000 do: n:=p^2+1: x:= factorset(n): n1:=nops(x): n2 :=bigomega(n): if n1=2 and n2 = 2 then zz:=x[1]+x[2]: T[k]:=zz: U[k]:=zz: V[k]:=p: k:=k+1: else fi: od:

# ascending sort

for i from 1 to k do: mini:=i :for j from i+1 to nn do: if T[j]< T[mini] then mini:=j: else fi: od: if mini<> i then x:=T[i]: T[i]:=T[mini]: T[mini]:=x: else fi: od:

# detection of identical sums

z:=1:for a from 1 to 52 do: if T[a]=T[a+1] or T[a]=T[a+1] or T[a]=T[a+2] or T[a]=T[a+3] or T[a]=T[a+4] or T[a]=T[a+5] then B[z]:=T[a]: z:=z+1: else fi: od: for d from 1 to 52 do: for e from 1 to 1000 do: if B[d]= U[e] then printf(`%d, `, V[e]): else fi: od: od:

PROG

(Sage)

def A181177_yield_vecs(max_sum):

....for s in [1..max_sum]:

........pqs = ((p, s-p) for p in prime_range(s//2) if is_prime(s-p) and (p != s-p))

........ss = list(sqrt(p*q-1) for p, q in pqs if is_square(p*q-1))

........if len(ss) > 1: yield ss

a = flatten(list(A181177_yield_vecs(2000))) # [D. S. McNeil, Jan 27 2011]

CROSSREFS

Sequence in context: A103320 A306882 A125526 * A124317 A254691 A159518

Adjacent sequences:  A181174 A181175 A181176 * A181178 A181179 A181180

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jan 25 2011

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)