A370351 The smallest number such that n or more numbers k exist such that k - a(n) = sopfr(k + a(n)), where sopfr(m) is the sum of the primes dividing m, with repetition.

1, 25, 55, 145, 487, 1585, 3995, 7795, 7795, 7795, 7795, 222785, 222785, 349065, 383905

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

a(1) = 1 as 1 is the smallest number to have one number (k = 7) such that 7 - 1 = 6 = sopfr(7 + 1) = sopfr(8) = 6.
a(2) = 25 as 25 is the smallest number to have two numbers (k = 38, 41) such that 38 - 25 = 13 = sopfr(38 + 25) = sopfr(63) = 13, and 41 - 25 = 16 = sopfr(41 + 25) = sopfr(66) = 16.
a(3) = 55 as 55 is the smallest number to have three numbers (k = 70, 75, 83) such that 70 - 55 = 15 = sopfr(70 + 55) = sopfr(125) = 15, 75 - 55 = 20 = sopfr(75 + 55) = sopfr(130) = 20, and 83 - 55 = 28 = sopfr(83 + 55) = sopfr(138) = 28.

Crossrefs

Cf. A001414, A369354, A369355, A370352.

Sequence in context: A091214 A338009 A036305 * A257708 A266817 A125827

Adjacent sequences: A370348 A370349 A370350 * A370352 A370353 A370354

Keyword

nonn,more

Author

Scott R. Shannon, Feb 16 2024

Status

approved