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A336098 Numbers k such that equation x = k*sopf(x) has no solutions in positive integers. 3
46, 55, 85, 87, 92, 110, 123, 138, 141, 145, 155, 158, 183, 184, 187, 190, 194, 203, 205, 217, 219, 220, 230, 238, 247, 253, 259, 261, 265, 275, 276, 282, 287, 290, 291, 295, 302, 305, 310, 316, 319, 327, 334, 339, 366, 368, 369, 380, 388, 391, 395, 403, 406, 407, 410, 414, 415, 423, 425, 426, 427, 434 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If k = p^s then p^(s+1) is solution of x = k*sopf(x). Hence powers of primes are not in the sequence.

Let p_1*...*p_t is in the sequence. Then p_1^a_1*...*p_t^a_t is in the sequence for all positive integers a_1, ..., a_t. It means that the sequence is infinite.

LINKS

Table of n, a(n) for n=1..62.

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

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; }

listako(nn) = {my(lim = pp(ip(nn))); my(v = vector(lim, k, k++; k/sopf(k))); my(w = vector(nn-1, k, #select(x->(x==k+1), v))); apply(x->(x+1), Vec(select(x->(x==0), w, 1))); } \\ Michel Marcus, Jul 16 2020

CROSSREFS

Cf. A008472, A336099.

Sequence in context: A039354 A043177 A043957 * A115444 A119385 A330243

Adjacent sequences:  A336095 A336096 A336097 * A336099 A336100 A336101

KEYWORD

nonn

AUTHOR

Vladimir Letsko, Jul 08 2020

STATUS

approved

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Last modified September 21 01:46 EDT 2021. Contains 347596 sequences. (Running on oeis4.)