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A268269 Primordial LB numbers: LB numbers (A267856) that are not of the form 10*n where n is also an LB number. 0
250, 375, 648, 972, 2430, 6750, 9375, 36450, 60750, 84672, 546750, 8346672, 12605250, 18907875, 26406250, 31513125, 39609375, 44118375, 53466750, 69328875, 81934125, 107144625, 119749875, 144960375, 182776125, 195381375, 233197125, 555644448, 579296448, 774927552, 833466672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

An LB number is a positive integer of the form n = a*10^k+b (with a > 0 and b < 10^k) satisfying two properties: 1) the set of prime factors of n is the union of the sets of prime factors of a and b; and 2) A001222(n) = A001222(a) + A001222(b) where A001222(n) = Bigomega(n) gives the number of primes divisors of n counted with multiplicity.

This sequence is an infinite subsequence of A267856.

a(13) > 10^7.

LINKS

Table of n, a(n) for n=1..31.

Robert O. Stanton, The Remarkable Number 648, Mathematics Magazine, Vol. 66, No. 1 (Feb., 1993), pp. 48-55.

EXAMPLE

972 is a term since 972 is an LB number (see A267856 for the reason) and 972 is not 10*k where k is an LB number.

2500 is an LB number but is not a term of this sequence since 2500 = 10*20 and 250 is an LB number.

PROG

(PARI) already(n, v) = {for (k=1, #v, q = n/v[k]; if (denominator(q) == 1, e = valuation(q, 10); if (q == 10^e, return (1)); ); ); }

isok(n) = {nb = #Str(n); spf = Set(factor(n)[, 1]~); nbpfr = bigomega(n); for (k=1, nb-1, a = n\10^k; b = n - 10^k*a; if (b && (bigomega(a)+ bigomega(b) == nbpfr) && (setunion(factor(a)[, 1]~, factor(b)[, 1]~) == spf), return (1)); ); }

lista(nn) = {my(v = []); for (n=1, nn, if (isok(n) && ! already(n, v), print1(n, ", "); v = concat(v, n); ); ); } \\ Michel Marcus, Jan 31 2016

CROSSREFS

Cf. A001222, A267856.

Sequence in context: A069154 A045169 A267856 * A045185 A122270 A234497

Adjacent sequences: A268266 A268267 A268268 * A268270 A268271 A268272

KEYWORD

nonn,base

AUTHOR

Tom Edgar, Jan 29 2016

EXTENSIONS

a(13)-a(31) from Michel Marcus, Jan 30 2016

STATUS

approved

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Last modified February 2 12:48 EST 2023. Contains 360021 sequences. (Running on oeis4.)