The On-Line Encyclopedia of Integer Sequences (OEIS)

A336297 revision #15

A336297

Prime numbers p such that equation x = p*sopf(x) (where sopf(x) is the sum of distinct prime factors of x) has exactly 1 solution in positive integers.

2, 61, 97, 113, 151, 173, 241, 277, 317, 353, 389, 449, 457, 593, 601, 607, 653, 673, 683, 727, 733, 797, 907, 929, 941, 947, 953, 977, 997, 1021, 1051, 1087, 1153, 1181, 1193, 1217, 1249, 1307, 1321, 1361, 1373, 1409, 1433, 1489, 1493, 1523, 1553, 1579, 1597, 1609, 1627

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

Vladimir Letsko, Mathematical Marathon, Problem 227 (in Russian).

EXAMPLE

4 is the unique integer x such that x = 2*sopf(x), a prime, so 2 is a term.

PROG

(PARI) sopf(n) = vecsum(factor(n)[, 1]); \\ A008472

pp(n) = prod(k=1, n, prime(k)); \\ A002110

sp(n) = sum(k=1, n, prime(k)); \\ A007504

ip(n) = {my(k=1); while (pp(k)/sp(k) <= n, k++); k+1; }

lista(nn) = {my(lim = pp(ip(nn))); my(v = vector(lim, k, k++; k/sopf(k))); my(w = select(x->myisprime(x), v)); select(x->(x<=nn), apply(x->prime(x), Vec(select(x->(x==1), vector(nn-1, k, #select(x->(x==prime(k)), w)), 1)))); } \\ Michel Marcus, Jul 19 2020

CROSSREFS

Cf. A008472, A336098, A336099, A336296.

Sequence in context: A364659 A222009 A351728 * A041449 A261944 A142729

Adjacent sequences: A336294 A336295 A336296 * A336298 A336299 A336300

KEYWORD

nonn

AUTHOR

Vladimir Letsko, Jul 16 2020

STATUS

proposed