A268269 Primordial LB numbers: LB numbers (A267856) that are not of the form 10*n where n is also an LB number.

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

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