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A175811 A007318-deficient numbers. 6
1, 7, 11, 13, 17, 18, 19, 23, 24, 25, 29, 30, 31, 32, 33, 37, 38, 39, 40, 41, 42, 43, 47, 48, 49, 50, 51, 52, 53, 57, 58, 59, 60, 61, 62, 63, 67, 68, 69, 70, 71, 72, 73, 74, 75, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Definition see in comment to A175522. The same criticism on index-selection as in A175807 applies. All primes greater than 5 are in the sequence.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

{n: sum_{d|n, d<n} A007318(d) < A007318(n)}.

MAPLE

A007318 := proc(n) option remember; local t, r; t := 0 ; for r from 0 do if t+r+1 > n then return binomial(r, n-t) ; end if; t := t+r+1 ; end do: end proc:

isA175811 := proc(n) m := 0 ; for d in numtheory[divisors](n) minus {n} do m := m+A007318(d) ; end do; m < A007318(n) ; end proc:

for n from 1 to 120 do if isA175811(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Dec 06 2010

PROG

(PARI) b(n) = {my(m = 1); while (m*(m+1)/2 < n, m++); if (! ispolygonal(n, 3), m--); binomial(m, n - m*(m+1)/2); }

isok(n) = sumdiv(n, d, (d<n)* b(d)) < b(n); \\ Michel Marcus, Feb 07 2016

CROSSREFS

Cf. A007318, A175522, A175807 (perfect version), A005100, A005101.

Sequence in context: A172120 A112090 A103487 * A112588 A191988 A128974

Adjacent sequences:  A175808 A175809 A175810 * A175812 A175813 A175814

KEYWORD

nonn,less

AUTHOR

Vladimir Shevelev, Dec 05 2010

EXTENSIONS

Terms >25 from R. J. Mathar, Dec 06 2010

STATUS

approved

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Last modified July 25 12:05 EDT 2021. Contains 346289 sequences. (Running on oeis4.)