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A172484 Partial sums of extravagant numbers, also called prodigal numbers, or wasteful numbers. 0
4, 10, 18, 27, 39, 57, 77, 99, 123, 149, 177, 207, 240, 274, 310, 348, 387, 427, 469, 513, 558, 604, 652, 702, 753, 805, 859, 914, 970, 1027, 1085, 1145, 1207, 1270, 1335, 1401, 1469, 1538, 1608, 1680, 1754, 1829, 1905, 1982, 2060, 2140, 2222, 2306, 2391, 2477 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every natural number, written in base 10, is either economical A046759 (also called frugal), or equidigital A046758, or extravagant (or prodigal or wasteful). An extravagant number is one for which the factorization requires more digits that the original number such as 30 = 2 * 3 * 5. The subsequence of economical partial sums of extravagant numbers begins: xxx, 18, 39, 57, 77, 99, 207, 240, 274, 310. The subsequence of equidigital partial sum of economical numbers begins: 10, 27, 123, 149, 177, 427, 469 (such as 1207 = 17 * 71). The subsequence of prime partial sums of economical numbers begins: xxx, 149, 859, 2477, 2833.

LINKS

Table of n, a(n) for n=1..50.

FORMULA

SUM[i=1..n] A046760(i) = Partial sum of {Write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n)>l(n)}.

EXAMPLE

a(1) = A046760(1) = 4. a(2) = 4 + 6 = 10. a(67) = 4 + 6 + 8 + 9 + 12 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 33 + 34 + 36 + 38 + 39 + 40 + 42 + 44 + 45 + 46 + 48 + 50 + 51 + 52 + 54 + 55 + 56 + 57 + 58 + 60 + 62 + 63 + 65 + 66 + 68 + 69 + 70 + 72 + 74 + 75 + 76 + 77 + 78 + 80 + 82 + 84 + 85 + 86 + 87 + 88 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 98 + 99 + 100 + 102 + 104 + 108 + 110 + 114 = 4138 = 2 * 2069 which is thus an economical number, with 4 digits but 5 in its prime factorization.

CROSSREFS

Cf. A046758, A046759, A046760.

Sequence in context: A225270 A073621 A048218 * A009876 A161958 A013921

Adjacent sequences:  A172481 A172482 A172483 * A172485 A172486 A172487

KEYWORD

base,easy,nonn

AUTHOR

Jonathan Vos Post, Feb 04 2010

EXTENSIONS

27 inserted by R. J. Mathar, Feb 06 2010

STATUS

approved

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Last modified July 20 22:20 EDT 2019. Contains 325189 sequences. (Running on oeis4.)