A372455 - OEIS

A372455

Smaller term of each Ruth-Aaron pair in which the sum of distinct prime factors is a prime number.

5, 24, 49, 714, 1682, 12726, 13775, 25839, 26642, 75140, 79118, 95709, 109939, 189080, 197657, 204258, 228599, 235586, 268656, 319428, 384312, 416119, 547525, 554682, 560150, 563390, 565823, 576984, 608316, 740726, 823150, 839375, 850746, 851709, 869054, 890723, 901747

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OFFSET

1,1

COMMENTS

A Ruth-Aaron pair consists of two consecutive integers (k,k+1) such that sopf(k) = sopf(k+1) where sopf(x) is the sum of the distinct prime factors of x (A008472).

The present sequence is those k for which this common sopf(k) = sopf(k+1) is prime.

LINKS

Table of n, a(n) for n=1..37.

Numberphile, Aaron Numbers.

Eric Weisstein's World of Mathematics, Ruth-Aaron Pair.

Wikipedia, Ruth-Aaron pair.

EXAMPLE

1682 is a term because the pair (1682, 1683) is a Ruth-Aaron pair with sum of prime factors 2 + 29 = 3 + 11 + 17 = 31 which is prime.

MAPLE

SumPF := n -> add(NumberTheory:-PrimeFactors(n)):

aList := proc(upto) local s0, s1, L, k; s0, s1 := 2, 3; L := NULL;

for k from 1 to upto do s0, s1 := s1, SumPF(k + 1);